diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 8528a4f013..f211577f94 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -866,6 +866,12 @@ component_check_test_cases () {
     fi
     tests/scripts/check_test_cases.py $opt
     unset opt
+
+    # Check that no tests are explicitely disabled when USE_PSA_CRYPTO is set
+    # as a matter of policy to ensure there is no missed testing
+    msg "Check: explicitely disabled test with USE_PSA_CRYPTO"  # < 1s
+    not grep -n 'depends_on:.*!MBEDTLS_USE_PSA_CRYPTO' tests/suites/*.function tests/suites/*.data
+    not grep -n '^ *requires_config_disabled.*MBEDTLS_USE_PSA_CRYPTO' tests/ssl-opt.sh tests/opt-testcases/*.sh
 }
 
 component_check_doxygen_warnings () {
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index bcbc0a0ebb..c106cf4edb 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -9975,7 +9975,6 @@ requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_SSL_ALPN
-requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
 run_test    "TLS 1.3: alpn - openssl" \
             "$O_NEXT_SRV -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache -alpn h2" \
             "$P_CLI debug_level=3 alpn=h2" \
@@ -10011,7 +10010,6 @@ requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_SSL_ALPN
-requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
 run_test    "TLS 1.3: alpn - gnutls" \
             "$G_NEXT_SRV --debug=4 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:%NO_TICKETS --disable-client-cert --alpn=h2" \
             "$P_CLI debug_level=3 alpn=h2" \
diff --git a/tests/suites/test_suite_pk.data b/tests/suites/test_suite_pk.data
index 306cfd7307..a0844ea2ed 100644
--- a/tests/suites/test_suite_pk.data
+++ b/tests/suites/test_suite_pk.data
@@ -185,12 +185,8 @@ Verify ext RSA #4 (PKCS1 v2.1, salt_len = max, OK)
 depends_on:MBEDTLS_PKCS1_V21:MBEDTLS_SHA256_C
 pk_rsa_verify_ext_test_vec:"54657374206d657373616765":MBEDTLS_MD_SHA256:1024:16:"00dd118a9f99bab068ca2aea3b6a6d5997ed4ec954e40deecea07da01eaae80ec2bb1340db8a128e891324a5c5f5fad8f590d7c8cacbc5fe931dafda1223735279461abaa0572b761631b3a8afe7389b088b63993a0a25ee45d21858bab9931aedd4589a631b37fcf714089f856549f359326dd1e0e86dde52ed66b4a90bda4095":16:"010001":"0d2bdb0456a3d651d5bd48a4204493898f72cf1aaddd71387cc058bc3f4c235ea6be4010fd61b28e1fbb275462b53775c04be9022d38b6a2e0387dddba86a3f8554d2858044a59fddbd594753fc056fe33c8daddb85dc70d164690b1182209ff84824e0be10e35c379f2f378bf176a9f7cb94d95e44d90276a298c8810f741c9":MBEDTLS_PK_RSASSA_PSS:MBEDTLS_MD_SHA256:94:128:0
 
-Verify ext RSA #5 using PSA (PKCS1 v2.1, wrong salt_len)
-depends_on:MBEDTLS_PKCS1_V21:MBEDTLS_SHA256_C:MBEDTLS_USE_PSA_CRYPTO
-pk_rsa_verify_ext_test_vec:"54657374206d657373616765":MBEDTLS_MD_SHA256:1024:16:"00dd118a9f99bab068ca2aea3b6a6d5997ed4ec954e40deecea07da01eaae80ec2bb1340db8a128e891324a5c5f5fad8f590d7c8cacbc5fe931dafda1223735279461abaa0572b761631b3a8afe7389b088b63993a0a25ee45d21858bab9931aedd4589a631b37fcf714089f856549f359326dd1e0e86dde52ed66b4a90bda4095":16:"010001":"0d2bdb0456a3d651d5bd48a4204493898f72cf1aaddd71387cc058bc3f4c235ea6be4010fd61b28e1fbb275462b53775c04be9022d38b6a2e0387dddba86a3f8554d2858044a59fddbd594753fc056fe33c8daddb85dc70d164690b1182209ff84824e0be10e35c379f2f378bf176a9f7cb94d95e44d90276a298c8810f741c9":MBEDTLS_PK_RSASSA_PSS:MBEDTLS_MD_SHA256:32:128:MBEDTLS_ERR_RSA_VERIFY_FAILED
-
 Verify ext RSA #5 (PKCS1 v2.1, wrong salt_len)
-depends_on:MBEDTLS_PKCS1_V21:MBEDTLS_SHA256_C:!MBEDTLS_USE_PSA_CRYPTO
+depends_on:MBEDTLS_PKCS1_V21:MBEDTLS_SHA256_C
 pk_rsa_verify_ext_test_vec:"54657374206d657373616765":MBEDTLS_MD_SHA256:1024:16:"00dd118a9f99bab068ca2aea3b6a6d5997ed4ec954e40deecea07da01eaae80ec2bb1340db8a128e891324a5c5f5fad8f590d7c8cacbc5fe931dafda1223735279461abaa0572b761631b3a8afe7389b088b63993a0a25ee45d21858bab9931aedd4589a631b37fcf714089f856549f359326dd1e0e86dde52ed66b4a90bda4095":16:"010001":"0d2bdb0456a3d651d5bd48a4204493898f72cf1aaddd71387cc058bc3f4c235ea6be4010fd61b28e1fbb275462b53775c04be9022d38b6a2e0387dddba86a3f8554d2858044a59fddbd594753fc056fe33c8daddb85dc70d164690b1182209ff84824e0be10e35c379f2f378bf176a9f7cb94d95e44d90276a298c8810f741c9":MBEDTLS_PK_RSASSA_PSS:MBEDTLS_MD_SHA256:32:128:MBEDTLS_ERR_RSA_INVALID_PADDING
 
 Verify ext RSA #6 (PKCS1 v2.1, MGF1 alg != MSG hash alg)
diff --git a/tests/suites/test_suite_pk.function b/tests/suites/test_suite_pk.function
index 8fd5367299..4b3af4c8da 100644
--- a/tests/suites/test_suite_pk.function
+++ b/tests/suites/test_suite_pk.function
@@ -487,6 +487,7 @@ void pk_rsa_verify_ext_test_vec( data_t * message_str, int digest,
     mbedtls_pk_rsassa_pss_options pss_opts;
     void *options;
     size_t hash_len;
+    int ret;
 
     USE_PSA_INIT( );
     mbedtls_pk_init( &pk );
@@ -526,9 +527,29 @@ void pk_rsa_verify_ext_test_vec( data_t * message_str, int digest,
         pss_opts.expected_salt_len = salt_len;
     }
 
-    TEST_ASSERT( mbedtls_pk_verify_ext( pk_type, options, &pk,
-                                digest, hash_result, hash_len,
-                                result_str->x, sig_len ) == result );
+    ret = mbedtls_pk_verify_ext( pk_type, options, &pk,
+                                 digest, hash_result, hash_len,
+                                 result_str->x, sig_len );
+
+#if defined(MBEDTLS_USE_PSA_CRYPTO)
+    if( result == MBEDTLS_ERR_RSA_INVALID_PADDING )
+    {
+        /* Mbed TLS distinguishes "invalid padding" from "valid padding but
+         * the rest of the signature is invalid". This has little use in
+         * practice and PSA doesn't report this distinction.
+         * In this case, PSA returns PSA_ERROR_INVALID_SIGNATURE translated
+         * to MBEDTLS_ERR_RSA_VERIFY_FAILED.
+         * However, currently `mbedtls_pk_verify_ext()` may use either the
+         * PSA or the Mbed TLS API, depending on the PSS options used.
+         * So, it may return either INVALID_PADDING or INVALID_SIGNATURE.
+         */
+        TEST_ASSERT( ret == result || ret == MBEDTLS_ERR_RSA_VERIFY_FAILED );
+    }
+    else
+#endif
+    {
+        TEST_EQUAL( ret, result );
+    }
 
 exit:
     mbedtls_pk_free( &pk );
diff --git a/tests/suites/test_suite_ssl.function b/tests/suites/test_suite_ssl.function
index 05656031d5..e42f8ba487 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -4844,7 +4844,7 @@ void ssl_session_serialize_version_check( int corrupt_major,
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_ENTROPY_C:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_ENTROPY_C:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void mbedtls_endpoint_sanity( int endpoint_type )
 {
     enum { BUFFSIZE = 1024 };
@@ -4867,13 +4867,15 @@ exit:
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_ENTROPY_C:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_ENTROPY_C:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void move_handshake_to_state(int endpoint_type, int state, int need_pass)
 {
     enum { BUFFSIZE = 1024 };
     mbedtls_endpoint base_ep, second_ep;
     int ret = -1;
 
+    USE_PSA_INIT( );
+
     ret = mbedtls_endpoint_init( &base_ep, endpoint_type, MBEDTLS_PK_RSA,
                                  NULL, NULL, NULL, NULL );
     TEST_ASSERT( ret == 0 );
@@ -4906,6 +4908,7 @@ void move_handshake_to_state(int endpoint_type, int state, int need_pass)
 exit:
     mbedtls_endpoint_free( &base_ep, NULL );
     mbedtls_endpoint_free( &second_ep, NULL );
+    USE_PSA_DONE( );
 }
 /* END_CASE */
 
@@ -4980,7 +4983,7 @@ void app_data( int mfl, int cli_msg_len, int srv_msg_len,
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void app_data_tls( int mfl, int cli_msg_len, int srv_msg_len,
                    int expected_cli_fragments,
                    int expected_srv_fragments )
@@ -4992,7 +4995,7 @@ void app_data_tls( int mfl, int cli_msg_len, int srv_msg_len,
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void app_data_dtls( int mfl, int cli_msg_len, int srv_msg_len,
                     int expected_cli_fragments,
                     int expected_srv_fragments )
@@ -5004,7 +5007,7 @@ void app_data_dtls( int mfl, int cli_msg_len, int srv_msg_len,
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_SSL_CONTEXT_SERIALIZATION:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_SSL_CONTEXT_SERIALIZATION:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void handshake_serialization( )
 {
     handshake_test_options options;
@@ -5018,7 +5021,7 @@ void handshake_serialization( )
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_DEBUG_C:MBEDTLS_SSL_MAX_FRAGMENT_LENGTH:MBEDTLS_CIPHER_MODE_CBC:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_DEBUG_C:MBEDTLS_SSL_MAX_FRAGMENT_LENGTH:MBEDTLS_CIPHER_MODE_CBC:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void handshake_fragmentation( int mfl, int expected_srv_hs_fragmentation, int expected_cli_hs_fragmentation)
 {
     handshake_test_options options;
@@ -5054,7 +5057,7 @@ void handshake_fragmentation( int mfl, int expected_srv_hs_fragmentation, int ex
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void renegotiation( int legacy_renegotiation )
 {
     handshake_test_options options;
@@ -5070,7 +5073,7 @@ void renegotiation( int legacy_renegotiation )
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void resize_buffers( int mfl, int renegotiation, int legacy_renegotiation,
                      int serialize, int dtls, char *cipher )
 {
@@ -5091,7 +5094,7 @@ void resize_buffers( int mfl, int renegotiation, int legacy_renegotiation,
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_CONTEXT_SERIALIZATION:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_CONTEXT_SERIALIZATION:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_SSL_PROTO_DTLS:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void resize_buffers_serialize_mfl( int mfl )
 {
     test_resize_buffers( mfl, 0, MBEDTLS_SSL_LEGACY_NO_RENEGOTIATION, 1, 1,
@@ -5102,7 +5105,7 @@ void resize_buffers_serialize_mfl( int mfl )
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_USE_PSA_CRYPTO:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
+/* BEGIN_CASE depends_on:MBEDTLS_X509_CRT_PARSE_C:!MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_PKCS1_V15:MBEDTLS_SSL_VARIABLE_BUFFER_LENGTH:MBEDTLS_SSL_RENEGOTIATION:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_RSA_C:MBEDTLS_ECP_DP_SECP384R1_ENABLED:MBEDTLS_ENTROPY_C:MBEDTLS_CTR_DRBG_C */
 void resize_buffers_renegotiate_mfl( int mfl, int legacy_renegotiation,
                                      char *cipher )
 {