diff --git a/library/ssl_tls13_server.c b/library/ssl_tls13_server.c
index 25279b3e34..9b273b834c 100644
--- a/library/ssl_tls13_server.c
+++ b/library/ssl_tls13_server.c
@@ -166,7 +166,6 @@ static int ssl_tls13_offered_psks_check_identity_match_ticket(
 {
     int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
     unsigned char *ticket_buffer;
-    unsigned int key_exchanges;
 #if defined(MBEDTLS_HAVE_TIME)
     mbedtls_ms_time_t now;
     mbedtls_ms_time_t server_age;
@@ -228,31 +227,6 @@ static int ssl_tls13_offered_psks_check_identity_match_ticket(
         goto exit;
     }
 
-    /* RFC 8446 section 4.2.9
-     *
-     * Servers SHOULD NOT send NewSessionTicket with tickets that are not
-     * compatible with the advertised modes; however, if a server does so,
-     * the impact will just be that the client's attempts at resumption fail.
-     *
-     * We regard the ticket with incompatible key exchange modes as not match.
-     */
-    MBEDTLS_SSL_PRINT_TICKET_FLAGS(4, session->ticket_flags);
-
-    key_exchanges = 0;
-    if (mbedtls_ssl_tls13_session_ticket_allow_psk_ephemeral(session) &&
-        ssl_tls13_key_exchange_is_psk_ephemeral_available(ssl)) {
-        key_exchanges |= MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL;
-    }
-    if (mbedtls_ssl_tls13_session_ticket_allow_psk(session) &&
-        ssl_tls13_key_exchange_is_psk_available(ssl)) {
-        key_exchanges |= MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK;
-    }
-
-    if (key_exchanges == 0) {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("No suitable key exchange mode"));
-        goto exit;
-    }
-
 #if defined(MBEDTLS_HAVE_TIME)
     now = mbedtls_ms_time();
 
@@ -543,6 +517,8 @@ static int ssl_tls13_parse_pre_shared_key_ext(
         int psk_type;
         int psk_ciphersuite_id;
         psa_algorithm_t psk_hash_alg;
+        int allowed_key_exchange_modes;
+        int key_exchange_mode = MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_NONE;
         const mbedtls_ssl_ciphersuite_t *ciphersuite_info;
 #if defined(MBEDTLS_SSL_SESSION_TICKETS)
         mbedtls_ssl_session session;
@@ -580,17 +556,38 @@ static int ssl_tls13_parse_pre_shared_key_ext(
             case MBEDTLS_SSL_TLS1_3_PSK_EXTERNAL:
                 psk_ciphersuite_id = 0;
                 psk_hash_alg = PSA_ALG_SHA_256;
+                allowed_key_exchange_modes =
+                    MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ALL;
                 break;
 #if defined(MBEDTLS_SSL_SESSION_TICKETS)
             case MBEDTLS_SSL_TLS1_3_PSK_RESUMPTION:
                 psk_ciphersuite_id = session.ciphersuite;
                 psk_hash_alg = PSA_ALG_NONE;
+                ssl->session_negotiate->ticket_flags = session.ticket_flags;
+                allowed_key_exchange_modes =
+                    session.ticket_flags &
+                    MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ALL;
                 break;
 #endif
             default:
                 return MBEDTLS_ERR_SSL_INTERNAL_ERROR;
         }
 
+        if ((allowed_key_exchange_modes &
+             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL) &&
+            ssl_tls13_key_exchange_is_psk_ephemeral_available(ssl)) {
+            key_exchange_mode = MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL;
+        } else if ((allowed_key_exchange_modes &
+                    MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK) &&
+                   ssl_tls13_key_exchange_is_psk_available(ssl)) {
+            key_exchange_mode = MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK;
+        }
+
+        if (key_exchange_mode == MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_NONE) {
+            MBEDTLS_SSL_DEBUG_MSG(3, ("No suitable PSK key exchange mode"));
+            continue;
+        }
+
         ssl_tls13_select_ciphersuite(ssl, ciphersuites, ciphersuites_end,
                                      psk_ciphersuite_id, psk_hash_alg,
                                      &ciphersuite_info);
@@ -664,7 +661,7 @@ static int ssl_tls13_parse_pre_shared_key_ext(
         return ret;
     }
     if (matched_identity == -1) {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("No matched PSK or ticket."));
+        MBEDTLS_SSL_DEBUG_MSG(3, ("No usable PSK or ticket."));
         return MBEDTLS_ERR_SSL_UNKNOWN_IDENTITY;
     }
 
diff --git a/tests/opt-testcases/tls13-kex-modes.sh b/tests/opt-testcases/tls13-kex-modes.sh
index 6556cd4b45..49f06e0715 100755
--- a/tests/opt-testcases/tls13-kex-modes.sh
+++ b/tests/opt-testcases/tls13-kex-modes.sh
@@ -23,7 +23,7 @@ run_test    "TLS 1.3: G->m: all/psk, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -s "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -41,7 +41,7 @@ run_test    "TLS 1.3: G->m: all/psk, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -78,7 +78,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/psk, good" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -s "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -96,7 +96,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/psk, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -133,7 +133,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/psk_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -151,7 +151,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/psk_ephemeral, fail, key id mismatch"
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -188,7 +188,7 @@ run_test    "TLS 1.3: G->m: all/psk_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -206,7 +206,7 @@ run_test    "TLS 1.3: G->m: all/psk_ephemeral, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -261,7 +261,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/psk_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -280,7 +280,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/psk_all, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -319,7 +319,7 @@ run_test    "TLS 1.3: G->m: all/psk_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -338,7 +338,7 @@ run_test    "TLS 1.3: G->m: all/psk_all, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -377,7 +377,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/psk_all, good" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -s "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -396,7 +396,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/psk_all, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -435,7 +435,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/ephemeral_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -454,7 +454,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/ephemeral_all, good, key id mismatch,
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -493,7 +493,7 @@ run_test    "TLS 1.3: G->m: all/ephemeral_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -512,7 +512,7 @@ run_test    "TLS 1.3: G->m: all/ephemeral_all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -550,8 +550,9 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/ephemeral_all, good" \
             -s "found pre_shared_key extension" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -s "No suitable PSK key exchange mode" \
+            -S "Pre shared key found" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -572,7 +573,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -592,7 +593,7 @@ run_test    "TLS 1.3: G->m: ephemeral_all/all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -633,7 +634,7 @@ run_test    "TLS 1.3: G->m: all/all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -653,7 +654,7 @@ run_test    "TLS 1.3: G->m: all/all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -694,7 +695,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/all, good" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -733,8 +734,9 @@ run_test    "TLS 1.3: G->m: ephemeral_all/psk_or_ephemeral, good" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -s "No suitable PSK key exchange mode" \
+            -S "Pre shared key found" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -754,7 +756,7 @@ run_test    "TLS 1.3: G->m: all/psk_or_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -793,7 +795,7 @@ run_test    "TLS 1.3: G->m: psk_or_ephemeral/psk_or_ephemeral, good" \
             -S "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -921,7 +923,7 @@ run_test    "TLS 1.3: O->m: all/psk, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -s "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -938,7 +940,7 @@ run_test    "TLS 1.3: O->m: all/psk, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -973,7 +975,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/psk_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -990,7 +992,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/psk_ephemeral, fail, key id mismatch"
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1025,7 +1027,7 @@ run_test    "TLS 1.3: O->m: all/psk_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1042,7 +1044,7 @@ run_test    "TLS 1.3: O->m: all/psk_ephemeral, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1078,7 +1080,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/psk_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1096,7 +1098,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/psk_all, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1133,7 +1135,7 @@ run_test    "TLS 1.3: O->m: all/psk_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1151,7 +1153,7 @@ run_test    "TLS 1.3: O->m: all/psk_all, fail, key id mismatch" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1188,7 +1190,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/ephemeral_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1206,7 +1208,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/ephemeral_all, good, key id mismatch,
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1243,7 +1245,7 @@ run_test    "TLS 1.3: O->m: all/ephemeral_all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1261,7 +1263,7 @@ run_test    "TLS 1.3: O->m: all/ephemeral_all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1299,7 +1301,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1318,7 +1320,7 @@ run_test    "TLS 1.3: O->m: ephemeral_all/all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1357,7 +1359,7 @@ run_test    "TLS 1.3: O->m: all/all, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -s "key exchange mode: psk_ephemeral"  \
             -S "key exchange mode: ephemeral"
@@ -1376,7 +1378,7 @@ run_test    "TLS 1.3: O->m: all/all, good, key id mismatch, dhe." \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1413,8 +1415,9 @@ run_test    "TLS 1.3: O->m: ephemeral_all/psk_or_ephemeral, good" \
             -s "found pre_shared_key extension" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -S "Found PSK KEX MODE" \
-            -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -s "No suitable PSK key exchange mode" \
+            -S "Pre shared key found" \
+            -s "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1433,7 +1436,7 @@ run_test    "TLS 1.3: O->m: all/psk_or_ephemeral, good" \
             -s "Found PSK_EPHEMERAL KEX MODE" \
             -s "Found PSK KEX MODE" \
             -s "Pre shared key found" \
-            -S "No matched PSK or ticket" \
+            -S "No usable PSK or ticket" \
             -S "key exchange mode: psk$"  \
             -S "key exchange mode: psk_ephemeral"  \
             -s "key exchange mode: ephemeral"
@@ -1580,7 +1583,7 @@ run_test    "TLS 1.3: m->m: psk/psk, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket"
+            -s "No usable PSK or ticket"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -1665,7 +1668,7 @@ run_test    "TLS 1.3: m->m: psk/psk_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -1711,7 +1714,7 @@ run_test    "TLS 1.3: m->m: psk/all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -1769,7 +1772,7 @@ run_test    "TLS 1.3: m->m: psk_ephemeral/psk_ephemeral, fail, key id mismatch"
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -1827,7 +1830,7 @@ run_test    "TLS 1.3: m->m: psk_ephemeral/ephemeral_all, fail, key id mismatch"
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket"
+            -s "No usable PSK or ticket"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -1870,7 +1873,7 @@ run_test    "TLS 1.3: m->m: psk_ephemeral/psk_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -1916,7 +1919,7 @@ run_test    "TLS 1.3: m->m: psk_ephemeral/all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -2047,7 +2050,7 @@ run_test    "TLS 1.3: m->m: ephemeral_all/psk_ephemeral, fail, key id mismatch"
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket"
+            -s "No usable PSK or ticket"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -2106,7 +2109,7 @@ run_test    "TLS 1.3: m->m: ephemeral_all/ephemeral_all,good,key id mismatch,fal
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "key exchange mode: ephemeral"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2152,7 +2155,7 @@ run_test    "TLS 1.3: m->m: ephemeral_all/psk_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2199,7 +2202,7 @@ run_test    "TLS 1.3: m->m: ephemeral_all/all, good, key id mismatch, fallback"
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "key exchange mode: ephemeral"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2288,7 +2291,7 @@ run_test    "TLS 1.3: m->m: psk_all/psk_ephemeral, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2348,7 +2351,7 @@ run_test    "TLS 1.3: m->m: psk_all/ephemeral_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket"
+            -s "No usable PSK or ticket"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -2392,7 +2395,7 @@ run_test    "TLS 1.3: m->m: psk_all/psk_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2438,7 +2441,7 @@ run_test    "TLS 1.3: m->m: psk_all/all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket"
+            -s "No usable PSK or ticket"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_SRV_C
@@ -2485,7 +2488,7 @@ run_test    "TLS 1.3: m->m: all/psk, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2532,7 +2535,7 @@ run_test    "TLS 1.3: m->m: all/psk_ephemeral, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2595,7 +2598,7 @@ run_test    "TLS 1.3: m->m: all/ephemeral_all, good, key id mismatch, fallback"
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -c "Selected key exchange mode: ephemeral" \
             -c "HTTP/1.0 200 OK"
 
@@ -2643,7 +2646,7 @@ run_test    "TLS 1.3: m->m: all/psk_all, fail, key id mismatch" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "ClientHello message misses mandatory extensions."
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
@@ -2690,7 +2693,7 @@ run_test    "TLS 1.3: m->m: all/all, good, key id mismatch, fallback" \
             -c "client hello, adding pre_shared_key extension, omitting PSK binder list" \
             -c "client hello, adding psk_key_exchange_modes extension" \
             -c "client hello, adding PSK binder list" \
-            -s "No matched PSK or ticket" \
+            -s "No usable PSK or ticket" \
             -s "key exchange mode: ephemeral"
 
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
diff --git a/tests/opt-testcases/tls13-misc.sh b/tests/opt-testcases/tls13-misc.sh
index ad062dccfb..3a21a745f3 100755
--- a/tests/opt-testcases/tls13-misc.sh
+++ b/tests/opt-testcases/tls13-misc.sh
@@ -353,8 +353,8 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk/none." \
          -s "key exchange mode: ephemeral" \
          -S "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: psk$" \
-         -s "No suitable key exchange mode" \
-         -s "No matched PSK or ticket"
+         -s "No suitable PSK key exchange mode" \
+         -s "No usable PSK or ticket"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_SSL_CLI_C MBEDTLS_DEBUG_C \
@@ -365,7 +365,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk/psk." \
          "$P_CLI debug_level=4 tls13_kex_modes=psk_or_ephemeral reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
@@ -381,8 +381,8 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk/psk_ephemeral." \
          -s "key exchange mode: ephemeral" \
          -S "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: psk$" \
-         -s "No suitable key exchange mode" \
-         -s "No matched PSK or ticket"
+         -s "No suitable PSK key exchange mode" \
+         -s "No usable PSK or ticket"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_SSL_CLI_C MBEDTLS_DEBUG_C \
@@ -393,7 +393,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk/psk_all." \
          "$P_CLI debug_level=4 tls13_kex_modes=psk_or_ephemeral reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
@@ -409,8 +409,8 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_ephemeral/none." \
          -s "key exchange mode: ephemeral" \
          -S "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: psk$" \
-         -s "No suitable key exchange mode" \
-         -s "No matched PSK or ticket"
+         -s "No suitable PSK key exchange mode" \
+         -s "No usable PSK or ticket"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_SSL_CLI_C MBEDTLS_DEBUG_C \
@@ -425,8 +425,8 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_ephemeral/psk." \
          -s "key exchange mode: ephemeral" \
          -S "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: psk$" \
-         -s "No suitable key exchange mode" \
-         -s "No matched PSK or ticket"
+         -s "No suitable PSK key exchange mode" \
+         -s "No usable PSK or ticket"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_SSL_CLI_C MBEDTLS_DEBUG_C \
@@ -437,7 +437,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_ephemeral/psk_ephemera
          "$P_CLI debug_level=4 tls13_kex_modes=ephemeral_all reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity" \
          -s "key exchange mode: psk_ephemeral"
 
@@ -450,7 +450,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_ephemeral/psk_all." \
          "$P_CLI debug_level=4 tls13_kex_modes=ephemeral_all reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity" \
          -s "key exchange mode: psk_ephemeral"
 
@@ -468,8 +468,8 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_all/none." \
          -s "key exchange mode: ephemeral" \
          -S "key exchange mode: psk_ephemeral" \
          -S "key exchange mode: psk$" \
-         -s "No suitable key exchange mode" \
-         -s "No matched PSK or ticket"
+         -s "No suitable PSK key exchange mode" \
+         -s "No usable PSK or ticket"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_SSL_CLI_C MBEDTLS_DEBUG_C \
@@ -481,7 +481,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_all/psk." \
          "$P_CLI debug_level=4 tls13_kex_modes=all reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity"
 
 requires_all_configs_enabled MBEDTLS_SSL_SESSION_TICKETS \
@@ -494,7 +494,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_all/psk_ephemeral." \
          "$P_CLI debug_level=4 tls13_kex_modes=all reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity" \
          -s "key exchange mode: psk_ephemeral"
 
@@ -508,7 +508,7 @@ run_test "TLS 1.3 m->m: Resumption with ticket flags, psk_all/psk_all." \
          "$P_CLI debug_level=4 tls13_kex_modes=all reconnect=1" \
          0 \
          -c "Pre-configured PSK number = 1" \
-         -S "No suitable key exchange mode" \
+         -S "No suitable PSK key exchange mode" \
          -s "found matched identity" \
          -s "key exchange mode: psk_ephemeral"