diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 5a284a60771f26..4db1b9ea6e0720 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1902,7 +1902,10 @@ class Http2Stream extends Duplex {
           !(state.flags & STREAM_FLAGS_HAS_TRAILERS) &&
           !state.didRead &&
           this._readableState.flowing === null) {
-        this.close();
+        // By using setImmediate we allow pushStreams to make it through
+        // before the stream is officially closed. This prevents a bug
+        // in most browsers where those pushStreams would be rejected.
+        setImmediate(this.close.bind(this));
       }
     }
   }
@@ -2137,7 +2140,7 @@ class ServerHttp2Stream extends Http2Stream {
     let headRequest = false;
     if (headers[HTTP2_HEADER_METHOD] === HTTP2_METHOD_HEAD)
       headRequest = options.endStream = true;
-    options.readable = !options.endStream;
+    options.readable = false;
 
     const headersList = mapToHeaders(headers);
     if (!Array.isArray(headersList))