diff --git a/lib/http2.c b/lib/http2.c
index 42f31290f..b8329d880 100644
--- a/lib/http2.c
+++ b/lib/http2.c
@@ -1120,6 +1120,7 @@ CURLcode Curl_http2_setup(struct connectdata *conn)
   httpc->upload_mem = NULL;
   httpc->upload_len = 0;
 
+  conn->bits.multiplex = TRUE; /* at least potentially multiplexed */
   conn->httpversion = 20;
   conn->bundle->server_supports_pipelining = TRUE;
 
diff --git a/lib/multi.c b/lib/multi.c
index a095238d5..5595bbd1f 100644
--- a/lib/multi.c
+++ b/lib/multi.c
@@ -1429,9 +1429,10 @@ static CURLMcode multi_runsingle(struct Curl_multi *multi,
 
     case CURLM_STATE_WAITPERFORM:
       /* Wait for our turn to PERFORM */
-      if(!data->easy_conn->readchannel_inuse &&
-         isHandleAtHead(data,
-                        data->easy_conn->recv_pipe)) {
+      if((!data->easy_conn->readchannel_inuse &&
+          isHandleAtHead(data,
+                         data->easy_conn->recv_pipe)) ||
+         data->easy_conn->bits.multiplex) {
         /* Grab the channel */
         data->easy_conn->readchannel_inuse = TRUE;
         multistate(data, CURLM_STATE_PERFORM);
diff --git a/lib/urldata.h b/lib/urldata.h
index 25fb98fe5..b09177e7a 100644
--- a/lib/urldata.h
+++ b/lib/urldata.h
@@ -530,6 +530,7 @@ struct ConnectBits {
   bool bound; /* set true if bind() has already been done on this socket/
                  connection */
   bool type_set;  /* type= was used in the URL */
+  bool multiplex; /* connection is multiplexed */
 };
 
 struct hostname {