diff --git a/lib/cfilters.c b/lib/cfilters.c
index 01f1e28218..6326f79f78 100644
--- a/lib/cfilters.c
+++ b/lib/cfilters.c
@@ -972,12 +972,15 @@ size_t Curl_conn_get_max_concurrent(struct Curl_easy *data,
                                     int sockindex)
 {
   CURLcode result;
-  int n = 0;
+  int n = -1;
 
   struct Curl_cfilter *cf = conn->cfilter[sockindex];
   result = cf ? cf->cft->query(cf, data, CF_QUERY_MAX_CONCURRENT,
                                &n, NULL) : CURLE_UNKNOWN_OPTION;
-  return (result || n <= 0) ? 1 : (size_t)n;
+  /* If no filter answered the query, the default is a non-multiplexed
+   * connection with limit 1. Otherwise, the the query may return 0
+   * for connections that are in shutdown, e.g. server HTTP/2 GOAWAY. */
+  return (result || n < 0) ? 1 : (size_t)n;
 }
 
 int Curl_conn_get_stream_error(struct Curl_easy *data,
diff --git a/lib/multi.c b/lib/multi.c
index 8543bfa8e5..b7f16a81c3 100644
--- a/lib/multi.c
+++ b/lib/multi.c
@@ -535,6 +535,22 @@ static void multi_done_locked(struct connectdata *conn,
                               void *userdata)
 {
   struct multi_done_ctx *mdctx = userdata;
+#ifndef CURL_DISABLE_VERBOSE_STRINGS
+  const char *host =
+#ifndef CURL_DISABLE_PROXY
+        conn->bits.socksproxy ?
+        conn->socks_proxy.host.dispname :
+        conn->bits.httpproxy ? conn->http_proxy.host.dispname :
+#endif
+        conn->bits.conn_to_host ? conn->conn_to_host.dispname :
+        conn->host.dispname;
+  int port =
+#ifndef CURL_DISABLE_PROXY
+        conn->bits.httpproxy ? conn->http_proxy.port :
+#endif
+        conn->bits.conn_to_port ? conn->conn_to_port :
+        conn->remote_port;
+#endif
 
   Curl_detach_connection(data);
 
@@ -580,30 +596,27 @@ static void multi_done_locked(struct connectdata *conn,
 #endif
      ) || conn->bits.close
        || (mdctx->premature && !Curl_conn_is_multiplex(conn, FIRSTSOCKET))) {
-    CURL_TRC_M(data, "multi_done, not reusing connection=%"
-                     FMT_OFF_T ", forbid=%d"
-                     ", close=%d, premature=%d, conn_multiplex=%d",
-                     conn->connection_id, data->set.reuse_forbid,
-                     conn->bits.close, mdctx->premature,
-                     Curl_conn_is_multiplex(conn, FIRSTSOCKET));
+    CURL_TRC_M(data, "multi_done, terminating conn #%" FMT_OFF_T " to %s:%d, "
+               "forbid=%d, close=%d, premature=%d, conn_multiplex=%d",
+               conn->connection_id, host, port, data->set.reuse_forbid,
+               conn->bits.close, mdctx->premature,
+               Curl_conn_is_multiplex(conn, FIRSTSOCKET));
     connclose(conn, "disconnecting");
     Curl_conn_terminate(data, conn, mdctx->premature);
   }
+  else if(!Curl_conn_get_max_concurrent(data, conn, FIRSTSOCKET)) {
+    CURL_TRC_M(data, "multi_done, conn #%" FMT_OFF_T " to %s:%d was shutdown"
+               " by server, not reusing", conn->connection_id, host, port);
+    connclose(conn, "server shutdown");
+    Curl_conn_terminate(data, conn, mdctx->premature);
+  }
   else {
     /* the connection is no longer in use by any transfer */
     if(Curl_cpool_conn_now_idle(data, conn)) {
       /* connection kept in the cpool */
-      const char *host =
-#ifndef CURL_DISABLE_PROXY
-        conn->bits.socksproxy ?
-        conn->socks_proxy.host.dispname :
-        conn->bits.httpproxy ? conn->http_proxy.host.dispname :
-#endif
-        conn->bits.conn_to_host ? conn->conn_to_host.dispname :
-        conn->host.dispname;
       data->state.lastconnect_id = conn->connection_id;
-      infof(data, "Connection #%" FMT_OFF_T " to host %s left intact",
-            conn->connection_id, host);
+      infof(data, "Connection #%" FMT_OFF_T " to host %s:%d left intact",
+            conn->connection_id, host, port);
     }
     else {
       /* connection was removed from the cpool and destroyed. */
diff --git a/tests/data/test1506 b/tests/data/test1506
index 90f1ed421c..d3cec05780 100644
--- a/tests/data/test1506
+++ b/tests/data/test1506
@@ -83,10 +83,10 @@ Accept: */*
 ^Host:.*
 </strip>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-* Connection #0 to host server1.example.com left intact
-* Connection #1 to host server2.example.com left intact
-* Connection #2 to host server3.example.com left intact
-* Connection #3 to host server4.example.com left intact
+* Connection #0 to host server1.example.com:%HTTPPORT left intact
+* Connection #1 to host server2.example.com:%HTTPPORT left intact
+* Connection #2 to host server3.example.com:%HTTPPORT left intact
+* Connection #3 to host server4.example.com:%HTTPPORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /Closing connection/))
diff --git a/tests/data/test1510 b/tests/data/test1510
index 23ef9517c9..236fbde3d9 100644
--- a/tests/data/test1510
+++ b/tests/data/test1510
@@ -83,10 +83,10 @@ Accept: */*
 ^Host:.*
 </strip>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-* Connection #0 to host server1.example.com left intact
-* Connection #1 to host server2.example.com left intact
-* Connection #2 to host server3.example.com left intact
-* Connection #3 to host server4.example.com left intact
+* Connection #0 to host server1.example.com:%HTTPPORT left intact
+* Connection #1 to host server2.example.com:%HTTPPORT left intact
+* Connection #2 to host server3.example.com:%HTTPPORT left intact
+* Connection #3 to host server4.example.com:%HTTPPORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /Closing connection/))
diff --git a/tests/data/test1542 b/tests/data/test1542
index 25df4a46e3..656af421df 100644
--- a/tests/data/test1542
+++ b/tests/data/test1542
@@ -55,11 +55,11 @@ Accept: */*
 
 </protocol>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-== Info: Connection #0 to host %HOSTIP left intact
-== Info: Connection #0 to host %HOSTIP left intact
-== Info: Connection #0 to host %HOSTIP left intact
+== Info: Connection #0 to host %HOSTIP:%HTTPPORT left intact
+== Info: Connection #0 to host %HOSTIP:%HTTPPORT left intact
+== Info: Connection #0 to host %HOSTIP:%HTTPPORT left intact
 == Info: shutting down connection #0
-== Info: Connection #1 to host %HOSTIP left intact
+== Info: Connection #1 to host %HOSTIP:%HTTPPORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /(closing|shutting down) connection #\d+/))
diff --git a/tests/data/test2402 b/tests/data/test2402
index 52c582415f..563443171a 100644
--- a/tests/data/test2402
+++ b/tests/data/test2402
@@ -96,10 +96,10 @@ Via: 2 nghttpx
 ^Host:.*
 </strip>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /Closing connection/))
diff --git a/tests/data/test2404 b/tests/data/test2404
index e7d68299ce..4ebcceac81 100644
--- a/tests/data/test2404
+++ b/tests/data/test2404
@@ -96,10 +96,10 @@ Via: 2 nghttpx
 ^Host:.*
 </strip>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
-* Connection #0 to host localhost left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
+* Connection #0 to host localhost:%HTTP2TLSPORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /Closing connection/))
diff --git a/tests/data/test2502 b/tests/data/test2502
index e86e6125ad..311b23deff 100644
--- a/tests/data/test2502
+++ b/tests/data/test2502
@@ -91,10 +91,10 @@ Via: 3 nghttpx
 ^Host:.*
 </strip>
 <file name="%LOGDIR/stderr%TESTNUMBER" mode="text">
-== Info: Connection #0 to host localhost left intact
-== Info: Connection #0 to host localhost left intact
-== Info: Connection #0 to host localhost left intact
-== Info: Connection #0 to host localhost left intact
+== Info: Connection #0 to host localhost:%HTTP3PORT left intact
+== Info: Connection #0 to host localhost:%HTTP3PORT left intact
+== Info: Connection #0 to host localhost:%HTTP3PORT left intact
+== Info: Connection #0 to host localhost:%HTTP3PORT left intact
 </file>
 <stripfile>
 $_ = '' if(($_ !~ /left intact/) && ($_ !~ /Closing connection/))