diff --git a/src/backend/libpq/be-secure.c b/src/backend/libpq/be-secure.c
index b391af34fb9..16422f60631 100644
--- a/src/backend/libpq/be-secure.c
+++ b/src/backend/libpq/be-secure.c
@@ -735,6 +735,13 @@ initialize_SSL(void)
 #endif
 		SSL_library_init();
 		SSL_load_error_strings();
+
+		/*
+		 * We use SSLv23_method() because it can negotiate use of the highest
+		 * mutually supported protocol version, while alternatives like
+		 * TLSv1_2_method() permit only one specific version.  Note that we
+		 * don't actually allow SSL v2, only v3 and TLS protocols (see below).
+		 */
 		SSL_context = SSL_CTX_new(SSLv23_method());
 		if (!SSL_context)
 			ereport(FATAL,
diff --git a/src/interfaces/libpq/fe-secure.c b/src/interfaces/libpq/fe-secure.c
index 51fa1a6f9ca..9a99b7ec70b 100644
--- a/src/interfaces/libpq/fe-secure.c
+++ b/src/interfaces/libpq/fe-secure.c
@@ -966,7 +966,13 @@ init_ssl_system(PGconn *conn)
 			SSL_load_error_strings();
 		}
 
-		SSL_context = SSL_CTX_new(TLSv1_method());
+		/*
+		 * We use SSLv23_method() because it can negotiate use of the highest
+		 * mutually supported protocol version, while alternatives like
+		 * TLSv1_2_method() permit only one specific version.  Note that we
+		 * don't actually allow SSL v2 or v3, only TLS protocols (see below).
+		 */
+		SSL_context = SSL_CTX_new(SSLv23_method());
 		if (!SSL_context)
 		{
 			char	   *err = SSLerrmessage();
@@ -981,6 +987,9 @@ init_ssl_system(PGconn *conn)
 			return -1;
 		}
 
+		/* Disable old protocol versions */
+		SSL_CTX_set_options(SSL_context, SSL_OP_NO_SSLv2 | SSL_OP_NO_SSLv3);
+
 		/*
 		 * Disable OpenSSL's moving-write-buffer sanity check, because it
 		 * causes unnecessary failures in nonblocking send cases.