diff --git a/lib/vtls/gtls.c b/lib/vtls/gtls.c
index 1a4bd004d..d61b4da9c 100644
--- a/lib/vtls/gtls.c
+++ b/lib/vtls/gtls.c
@@ -314,9 +314,12 @@ set_ssl_version_min_max(const char **prioritylist, struct Curl_easy *data)
   long ssl_version = SSL_CONN_CONFIG(version);
   long ssl_version_max = SSL_CONN_CONFIG(version_max);
 
-  if(ssl_version_max == CURL_SSLVERSION_MAX_NONE) {
+  if((ssl_version == CURL_SSLVERSION_DEFAULT) ||
+     (ssl_version == CURL_SSLVERSION_TLSv1))
+    ssl_version = CURL_SSLVERSION_TLSv1_0;
+  if(ssl_version_max == CURL_SSLVERSION_MAX_NONE)
     ssl_version_max = CURL_SSLVERSION_MAX_DEFAULT;
-  }
+
   switch(ssl_version | ssl_version_max) {
   case CURL_SSLVERSION_TLSv1_0 | CURL_SSLVERSION_MAX_TLSv1_0:
     *prioritylist = GNUTLS_CIPHERS ":-VERS-SSL3.0:-VERS-TLS-ALL:"
@@ -546,29 +549,20 @@ gtls_connect_step1(struct Curl_easy *data,
    * removed if a run-time error indicates that SRP is not supported by this
    * GnuTLS version */
   switch(SSL_CONN_CONFIG(version)) {
-    case CURL_SSLVERSION_SSLv3:
-      prioritylist = GNUTLS_CIPHERS ":-VERS-TLS-ALL:+VERS-SSL3.0";
-      break;
     case CURL_SSLVERSION_DEFAULT:
     case CURL_SSLVERSION_TLSv1:
-      prioritylist = GNUTLS_CIPHERS ":-VERS-SSL3.0"
-#ifdef HAS_TLS13
-                     ":+VERS-TLS1.3"
-#endif
-                     ;
-      break;
     case CURL_SSLVERSION_TLSv1_0:
     case CURL_SSLVERSION_TLSv1_1:
     case CURL_SSLVERSION_TLSv1_2:
-    case CURL_SSLVERSION_TLSv1_3:
-      {
-        CURLcode result = set_ssl_version_min_max(&prioritylist, data);
-        if(result != CURLE_OK)
-          return result;
-        break;
-      }
+    case CURL_SSLVERSION_TLSv1_3: {
+      CURLcode result = set_ssl_version_min_max(&prioritylist, data);
+      if(result)
+        return result;
+      break;
+    }
     case CURL_SSLVERSION_SSLv2:
-      failf(data, "GnuTLS does not support SSLv2");
+    case CURL_SSLVERSION_SSLv3:
+      failf(data, "GnuTLS does not support SSLv2 or SSLv3");
       return CURLE_SSL_CONNECT_ERROR;
     default:
       failf(data, "Unrecognized parameter passed via CURLOPT_SSLVERSION");