diff --git a/transport/internet/splithttp/client.go b/transport/internet/splithttp/client.go
index 2a467d7d..8330d5d7 100644
--- a/transport/internet/splithttp/client.go
+++ b/transport/internet/splithttp/client.go
@@ -94,6 +94,10 @@ func (c *DefaultDialerClient) OpenDownload(ctx context.Context, baseURL string)
 		gotDownResponse.Close()
 	}()
 
+	if c.isH3 {
+		gotConn.Close()
+	}
+
 	// we want to block Dial until we know the remote address of the server,
 	// for logging purposes
 	<-gotConn.Wait()