diff --git a/tests/auto/network/access/http2/http2srv.cpp b/tests/auto/network/access/http2/http2srv.cpp
index 1f9ffb8985..6e2220fa67 100644
--- a/tests/auto/network/access/http2/http2srv.cpp
+++ b/tests/auto/network/access/http2/http2srv.cpp
@@ -431,6 +431,13 @@ void Http2Server::readReady()
     if (connectionError)
         return;
 
+    if (redirectSent) {
+        // We are a "single shot" server, working in 'h2' mode,
+        // responding with a redirect code. Don't bother to handle
+        // anything else now.
+        return;
+    }
+
     if (upgradeProtocol) {
         handleProtocolUpgrade();
     } else if (waitingClientPreface) {
@@ -800,6 +807,13 @@ void Http2Server::sendResponse(quint32 streamID, bool emptyBody)
 
     HttpHeader header;
     if (redirectWhileReading) {
+        if (redirectSent) {
+            // This is a "single-shot" server responding with a redirect code.
+            return;
+        }
+
+        redirectSent = true;
+
         qDebug("server received HEADERS frame (followed by DATA frames), redirecting ...");
         Q_ASSERT(targetPort);
         header.push_back({":status", "308"});
diff --git a/tests/auto/network/access/http2/http2srv.h b/tests/auto/network/access/http2/http2srv.h
index 87a17ced8b..ae3f084fdc 100644
--- a/tests/auto/network/access/http2/http2srv.h
+++ b/tests/auto/network/access/http2/http2srv.h
@@ -193,6 +193,7 @@ private:
     // Redirect, with status code 308, as soon as we've seen headers, while client
     // may still be sending DATA frames.  See tst_Http2::earlyResponse().
     bool redirectWhileReading = false;
+    bool redirectSent = false;
     quint16 targetPort = 0;
     QAtomicInt interrupted;
 protected slots:
diff --git a/tests/auto/network/access/http2/tst_http2.cpp b/tests/auto/network/access/http2/tst_http2.cpp
index 235b78c34a..52e98c1fc1 100644
--- a/tests/auto/network/access/http2/tst_http2.cpp
+++ b/tests/auto/network/access/http2/tst_http2.cpp
@@ -473,7 +473,7 @@ void tst_Http2::earlyResponse()
     runEventLoop();
 
     QVERIFY(serverPort);
-    sendRequest(1, QNetworkRequest::NormalPriority, {10000000, Qt::Uninitialized});
+    sendRequest(1, QNetworkRequest::NormalPriority, {1000000, Qt::Uninitialized});
 
     runEventLoop();