diff --git a/lib/connect.c b/lib/connect.c
index 5dc4e2fc74..e3295524b0 100644
--- a/lib/connect.c
+++ b/lib/connect.c
@@ -123,7 +123,7 @@ timediff_t Curl_timeleft(struct Curl_easy *data,
      before the connect timeout expires and we must acknowledge whichever
      timeout that is reached first. The total timeout is set per entire
      operation, while the connect timeout is set per connect. */
-  if(data->set.timeout <= 0 && !duringconnect)
+  if((!data->set.timeout || data->set.connect_only) && !duringconnect)
     return 0; /* no timeout in place or checked, return "no limit" */
 
   if(!nowp) {
@@ -131,9 +131,9 @@ timediff_t Curl_timeleft(struct Curl_easy *data,
     nowp = &now;
   }
 
-  if(data->set.timeout > 0) {
+  if(data->set.timeout) {
     timeleft_ms = data->set.timeout -
-                  curlx_timediff(*nowp, data->progress.t_startop);
+      curlx_timediff(*nowp, data->progress.t_startop);
     if(!timeleft_ms)
       timeleft_ms = -1; /* 0 is "no limit", fake 1 ms expiry */
     if(!duringconnect)
diff --git a/lib/pingpong.c b/lib/pingpong.c
index 3f6da71eae..0a15e33f0a 100644
--- a/lib/pingpong.c
+++ b/lib/pingpong.c
@@ -64,7 +64,7 @@ timediff_t Curl_pp_state_timeout(struct Curl_easy *data,
      full response to arrive before we bail out */
   timeout_ms = response_time - curlx_timediff(now, pp->response);
 
-  if((data->set.timeout > 0) && !disconnecting) {
+  if(data->set.timeout && !disconnecting) {
     /* if timeout is requested, find out how much overall remains */
     timediff_t timeout2_ms = Curl_timeleft(data, &now, FALSE);
     /* pick the lowest number */