diff --git a/contrib/sslinfo/sslinfo.c b/contrib/sslinfo/sslinfo.c
index da702011193..9191bbce5dc 100644
--- a/contrib/sslinfo/sslinfo.c
+++ b/contrib/sslinfo/sslinfo.c
@@ -24,8 +24,8 @@ PG_MODULE_MAGIC_EXT(
 					.version = PG_VERSION
 );
 
-static Datum X509_NAME_field_to_text(X509_NAME *name, text *fieldName);
-static Datum ASN1_STRING_to_text(ASN1_STRING *str);
+static Datum X509_NAME_field_to_text(const X509_NAME *name, text *fieldName);
+static Datum ASN1_STRING_to_text(const ASN1_STRING *str);
 
 /*
  * Function context for data persisting over repeated calls.
@@ -148,7 +148,7 @@ ssl_client_serial(PG_FUNCTION_ARGS)
  * function.
  */
 static Datum
-ASN1_STRING_to_text(ASN1_STRING *str)
+ASN1_STRING_to_text(const ASN1_STRING *str)
 {
 	BIO		   *membuf;
 	size_t		size;
@@ -194,12 +194,12 @@ ASN1_STRING_to_text(ASN1_STRING *str)
  * part of name
  */
 static Datum
-X509_NAME_field_to_text(X509_NAME *name, text *fieldName)
+X509_NAME_field_to_text(const X509_NAME *name, text *fieldName)
 {
 	char	   *string_fieldname;
 	int			nid,
 				index;
-	ASN1_STRING *data;
+	const ASN1_STRING *data;
 
 	string_fieldname = text_to_cstring(fieldName);
 	nid = OBJ_txt2nid(string_fieldname);
@@ -209,7 +209,7 @@ X509_NAME_field_to_text(X509_NAME *name, text *fieldName)
 				 errmsg("invalid X.509 field name: \"%s\"",
 						string_fieldname)));
 	pfree(string_fieldname);
-	index = X509_NAME_get_index_by_NID(name, nid, -1);
+	index = X509_NAME_get_index_by_NID(unconstify(X509_NAME *, name), nid, -1);
 	if (index < 0)
 		return (Datum) 0;
 	data = X509_NAME_ENTRY_get_data(X509_NAME_get_entry(name, index));
@@ -421,8 +421,8 @@ ssl_extension_info(PG_FUNCTION_ARGS)
 		HeapTuple	tuple;
 		Datum		result;
 		BIO		   *membuf;
-		X509_EXTENSION *ext;
-		ASN1_OBJECT *obj;
+		const X509_EXTENSION *ext;
+		const ASN1_OBJECT *obj;
 		int			nid;
 		int			len;
 
@@ -435,7 +435,7 @@ ssl_extension_info(PG_FUNCTION_ARGS)
 
 		/* Get the extension from the certificate */
 		ext = X509_get_ext(cert, call_cntr);
-		obj = X509_EXTENSION_get_object(ext);
+		obj = X509_EXTENSION_get_object(unconstify(X509_EXTENSION *, ext));
 
 		/* Get the extension name */
 		nid = OBJ_obj2nid(obj);
@@ -448,7 +448,7 @@ ssl_extension_info(PG_FUNCTION_ARGS)
 		nulls[0] = false;
 
 		/* Get the extension value */
-		if (X509V3_EXT_print(membuf, ext, 0, 0) <= 0)
+		if (X509V3_EXT_print(membuf, unconstify(X509_EXTENSION *, ext), 0, 0) <= 0)
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("could not print extension value in certificate at position %d",
diff --git a/src/backend/libpq/be-secure-openssl.c b/src/backend/libpq/be-secure-openssl.c
index c8b63ef8249..b67b91a54b2 100644
--- a/src/backend/libpq/be-secure-openssl.c
+++ b/src/backend/libpq/be-secure-openssl.c
@@ -78,7 +78,7 @@ static bool initialize_ecdh(SSL_CTX *context, bool isServerStart);
 static const char *SSLerrmessageExt(unsigned long ecode, const char *replacement);
 static const char *SSLerrmessage(unsigned long ecode);
 
-static char *X509_NAME_to_cstring(X509_NAME *name);
+static char *X509_NAME_to_cstring(const X509_NAME *name);
 
 static SSL_CTX *SSL_context = NULL;
 static bool dummy_ssl_passwd_cb_called = false;
@@ -638,18 +638,18 @@ aloop:
 	if (port->peer != NULL)
 	{
 		int			len;
-		X509_NAME  *x509name = X509_get_subject_name(port->peer);
+		const X509_NAME *x509name = X509_get_subject_name(port->peer);
 		char	   *peer_dn;
 		BIO		   *bio = NULL;
 		BUF_MEM    *bio_buf = NULL;
 
-		len = X509_NAME_get_text_by_NID(x509name, NID_commonName, NULL, 0);
+		len = X509_NAME_get_text_by_NID(unconstify(X509_NAME *, x509name), NID_commonName, NULL, 0);
 		if (len != -1)
 		{
 			char	   *peer_cn;
 
 			peer_cn = MemoryContextAlloc(TopMemoryContext, len + 1);
-			r = X509_NAME_get_text_by_NID(x509name, NID_commonName, peer_cn,
+			r = X509_NAME_get_text_by_NID(unconstify(X509_NAME *, x509name), NID_commonName, peer_cn,
 										  len + 1);
 			peer_cn[len] = '\0';
 			if (r != len)
@@ -1642,14 +1642,14 @@ be_tls_get_certificate_hash(Port *port, size_t *len)
  *
  */
 static char *
-X509_NAME_to_cstring(X509_NAME *name)
+X509_NAME_to_cstring(const X509_NAME *name)
 {
 	BIO		   *membuf = BIO_new(BIO_s_mem());
 	int			i,
 				nid,
 				count = X509_NAME_entry_count(name);
-	X509_NAME_ENTRY *e;
-	ASN1_STRING *v;
+	const X509_NAME_ENTRY *e;
+	const ASN1_STRING *v;
 	const char *field_name;
 	size_t		size;
 	char		nullterm;
diff --git a/src/interfaces/libpq/fe-secure-openssl.c b/src/interfaces/libpq/fe-secure-openssl.c
index d2045c73ae6..1dd9ba2f506 100644
--- a/src/interfaces/libpq/fe-secure-openssl.c
+++ b/src/interfaces/libpq/fe-secure-openssl.c
@@ -67,7 +67,7 @@
 
 static int	verify_cb(int ok, X509_STORE_CTX *ctx);
 static int	openssl_verify_peer_name_matches_certificate_name(PGconn *conn,
-															  ASN1_STRING *name_entry,
+															  const ASN1_STRING *name_entry,
 															  char **store_name);
 static int	openssl_verify_peer_name_matches_certificate_ip(PGconn *conn,
 															ASN1_OCTET_STRING *addr_entry,
@@ -467,7 +467,8 @@ cert_cb(SSL *ssl, void *arg)
  * into a plain C string.
  */
 static int
-openssl_verify_peer_name_matches_certificate_name(PGconn *conn, ASN1_STRING *name_entry,
+openssl_verify_peer_name_matches_certificate_name(PGconn *conn,
+												  const ASN1_STRING *name_entry,
 												  char **store_name)
 {
 	int			len;
@@ -650,14 +651,14 @@ pgtls_verify_peer_name_matches_certificate_guts(PGconn *conn,
 	 */
 	if (check_cn)
 	{
-		X509_NAME  *subject_name;
+		const X509_NAME *subject_name;
 
 		subject_name = X509_get_subject_name(conn->peer);
 		if (subject_name != NULL)
 		{
 			int			cn_index;
 
-			cn_index = X509_NAME_get_index_by_NID(subject_name,
+			cn_index = X509_NAME_get_index_by_NID(unconstify(X509_NAME *, subject_name),
 												  NID_commonName, -1);
 			if (cn_index >= 0)
 			{
diff --git a/src/test/ssl/t/001_ssltests.pl b/src/test/ssl/t/001_ssltests.pl
index 310d70a4c08..973399b63d0 100644
--- a/src/test/ssl/t/001_ssltests.pl
+++ b/src/test/ssl/t/001_ssltests.pl
@@ -819,7 +819,7 @@ $node->connect_fails(
 	"$common_connstr user=ssltestuser sslcert=ssl/client-revoked.crt "
 	  . sslkey('client-revoked.key'),
 	"certificate authorization fails with revoked client cert",
-	expected_stderr => qr|SSL error: ssl[a-z0-9/]* alert certificate revoked|,
+	expected_stderr => qr!SSL error: (ssl[a-z0-9/]*|tls) alert certificate revoked!,
 	log_like => [
 		qr{Client certificate verification failed at depth 0: certificate revoked},
 		qr{Failed certificate data \(unverified\): subject "/CN=ssltestuser", serial number \d+, issuer "/CN=Test CA for PostgreSQL SSL regression test client certs"},
@@ -921,7 +921,7 @@ $node->connect_fails(
 	"$common_connstr user=ssltestuser sslcert=ssl/client-revoked.crt "
 	  . sslkey('client-revoked.key'),
 	"certificate authorization fails with revoked client cert with server-side CRL directory",
-	expected_stderr => qr|SSL error: ssl[a-z0-9/]* alert certificate revoked|,
+	expected_stderr => qr!SSL error: (ssl[a-z0-9/]*|tls) alert certificate revoked!,
 	log_like => [
 		qr{Client certificate verification failed at depth 0: certificate revoked},
 		qr{Failed certificate data \(unverified\): subject "/CN=ssltestuser", serial number \d+, issuer "/CN=Test CA for PostgreSQL SSL regression test client certs"},
@@ -932,7 +932,7 @@ $node->connect_fails(
 	"$common_connstr user=ssltestuser sslcert=ssl/client-revoked-utf8.crt "
 	  . sslkey('client-revoked-utf8.key'),
 	"certificate authorization fails with revoked UTF-8 client cert with server-side CRL directory",
-	expected_stderr => qr|SSL error: ssl[a-z0-9/]* alert certificate revoked|,
+	expected_stderr => qr!SSL error: (ssl[a-z0-9/]*|tls) alert certificate revoked!,
 	log_like => [
 		qr{Client certificate verification failed at depth 0: certificate revoked},
 		qr{Failed certificate data \(unverified\): subject "/CN=\\xce\\x9f\\xce\\xb4\\xcf\\x85\\xcf\\x83\\xcf\\x83\\xce\\xad\\xce\\xb1\\xcf\\x82", serial number \d+, issuer "/CN=Test CA for PostgreSQL SSL regression test client certs"},