diff --git a/tests/http/test_07_upload.py b/tests/http/test_07_upload.py
index 40599c6ebe..dc28f2f4cf 100644
--- a/tests/http/test_07_upload.py
+++ b/tests/http/test_07_upload.py
@@ -414,6 +414,8 @@ class TestUpload:
     def test_07_36_upload_30x(self, env: Env, httpd, nghttpx, redir, proto):
         if proto == 'h3' and not env.have_h3():
             pytest.skip("h3 not supported")
+        if proto == 'h3' and env.curl_uses_ossl_quic():
+            pytest.skip("OpenSSL's own QUIC is flaky here")
         if proto == 'h3' and env.curl_uses_lib('msh3'):
             pytest.skip("msh3 fails here")
         data = '0123456789' * 10
@@ -431,6 +433,8 @@ class TestUpload:
     def test_07_37_upload_307(self, env: Env, httpd, nghttpx, proto):
         if proto == 'h3' and not env.have_h3():
             pytest.skip("h3 not supported")
+        if proto == 'h3' and env.curl_uses_ossl_quic():
+            pytest.skip("OpenSSL's own QUIC is flaky here")
         if proto == 'h3' and env.curl_uses_lib('msh3'):
             pytest.skip("msh3 fails here")
         data = '0123456789' * 10