diff --git a/lib/urldata.h b/lib/urldata.h
index c359c06d0..a2dc1c362 100644
--- a/lib/urldata.h
+++ b/lib/urldata.h
@@ -288,6 +288,9 @@ struct ssl_connect_data {
      current state of the connection. */
   bool use;
   ssl_connection_state state;
+#ifdef USE_NGHTTP2
+  bool asked_for_h2;
+#endif
 #ifdef USE_SSLEAY
   /* these ones requires specific SSL-types */
   SSL_CTX* ctx;
diff --git a/lib/vtls/gtls.c b/lib/vtls/gtls.c
index 434f872ff..a9c42c2d8 100644
--- a/lib/vtls/gtls.c
+++ b/lib/vtls/gtls.c
@@ -618,6 +618,7 @@ gtls_connect_step1(struct connectdata *conn,
       gnutls_alpn_set_protocols(session, protocols, protocols_size, 0);
       infof(data, "ALPN, offering %s, %s\n", NGHTTP2_PROTO_VERSION_ID,
             ALPN_HTTP_1_1);
+      connssl->asked_for_h2 = TRUE;
     }
     else {
       infof(data, "SSL, can't negotiate HTTP/2.0 without ALPN\n");
@@ -1047,7 +1048,7 @@ gtls_connect_step3(struct connectdata *conn,
         conn->negnpn = NPN_HTTP1_1;
       }
     }
-    else {
+    else if(connssl->asked_for_h2) {
       infof(data, "ALPN, server did not agree to a protocol\n");
     }
   }
diff --git a/lib/vtls/nss.c b/lib/vtls/nss.c
index 8161b434d..f26cba0d4 100644
--- a/lib/vtls/nss.c
+++ b/lib/vtls/nss.c
@@ -665,18 +665,19 @@ static void HandshakeCallback(PRFileDesc *sock, void *arg)
   if(SSL_GetNextProto(sock, &state, buf, &buflen, buflenmax) == SECSuccess) {
 
     switch(state) {
-      case SSL_NEXT_PROTO_NO_SUPPORT:
-      case SSL_NEXT_PROTO_NO_OVERLAP:
+    case SSL_NEXT_PROTO_NO_SUPPORT:
+    case SSL_NEXT_PROTO_NO_OVERLAP:
+      if(connssl->asked_for_h2)
         infof(conn->data, "TLS, neither ALPN nor NPN succeeded\n");
-        return;
+      return;
 #ifdef SSL_ENABLE_ALPN
-      case SSL_NEXT_PROTO_SELECTED:
-        infof(conn->data, "ALPN, server accepted to use %.*s\n", buflen, buf);
-        break;
+    case SSL_NEXT_PROTO_SELECTED:
+      infof(conn->data, "ALPN, server accepted to use %.*s\n", buflen, buf);
+      break;
 #endif
-      case SSL_NEXT_PROTO_NEGOTIATED:
-        infof(conn->data, "NPN, server accepted to use %.*s\n", buflen, buf);
-        break;
+    case SSL_NEXT_PROTO_NEGOTIATED:
+      infof(conn->data, "NPN, server accepted to use %.*s\n", buflen, buf);
+      break;
     }
 
     if(buflen == NGHTTP2_PROTO_VERSION_ID_LEN &&
@@ -1639,6 +1640,7 @@ static CURLcode nss_setup_connect(struct connectdata *conn, int sockindex)
       if(SSL_SetNextProtoNego(connssl->handle, alpn_protos, alpn_protos_len)
           != SECSuccess)
         goto error;
+      connssl->asked_for_h2 = TRUE;
     }
     else {
       infof(data, "SSL, can't negotiate HTTP/2.0 with neither NPN nor ALPN\n");
diff --git a/lib/vtls/openssl.c b/lib/vtls/openssl.c
index ccf2f738b..4bd7d0aaf 100644
--- a/lib/vtls/openssl.c
+++ b/lib/vtls/openssl.c
@@ -1742,6 +1742,7 @@ static CURLcode ossl_connect_step1(struct connectdata *conn, int sockindex)
 
       infof(data, "ALPN, offering %s, %s\n", NGHTTP2_PROTO_VERSION_ID,
             ALPN_HTTP_1_1);
+      connssl->asked_for_h2 = TRUE;
     }
 #endif
   }
@@ -2028,14 +2029,16 @@ static CURLcode ossl_connect_step2(struct connectdata *conn, int sockindex)
 
         if(len == NGHTTP2_PROTO_VERSION_ID_LEN &&
            memcmp(NGHTTP2_PROTO_VERSION_ID, neg_protocol, len) == 0) {
-             conn->negnpn = NPN_HTTP2;
+          conn->negnpn = NPN_HTTP2;
         }
-        else if(len == ALPN_HTTP_1_1_LENGTH && memcmp(ALPN_HTTP_1_1,
-            neg_protocol, ALPN_HTTP_1_1_LENGTH) == 0) {
+        else if(len ==
+                ALPN_HTTP_1_1_LENGTH && memcmp(ALPN_HTTP_1_1,
+                                               neg_protocol,
+                                               ALPN_HTTP_1_1_LENGTH) == 0) {
           conn->negnpn = NPN_HTTP1_1;
         }
       }
-      else
+      else if(connssl->asked_for_h2)
         infof(data, "ALPN, server did not agree to a protocol\n");
     }
 #endif
diff --git a/lib/vtls/polarssl.c b/lib/vtls/polarssl.c
index a9ea1e528..822617846 100644
--- a/lib/vtls/polarssl.c
+++ b/lib/vtls/polarssl.c
@@ -358,6 +358,7 @@ polarssl_connect_step1(struct connectdata *conn,
       ssl_set_alpn_protocols(&connssl->ssl, protocols);
       infof(data, "ALPN, offering %s, %s\n", protocols[0],
             protocols[1]);
+      connssl->asked_for_h2 = TRUE;
     }
   }
 #endif
@@ -466,7 +467,7 @@ polarssl_connect_step2(struct connectdata *conn,
         conn->negnpn = NPN_HTTP1_1;
       }
     }
-    else {
+    else if(connssl->asked_for_h2) {
       infof(data, "ALPN, server did not agree to a protocol\n");
     }
   }