diff --git a/ext/test/http/curl_http_test.cc b/ext/test/http/curl_http_test.cc
index 90142962d..9a5f58413 100644
--- a/ext/test/http/curl_http_test.cc
+++ b/ext/test/http/curl_http_test.cc
@@ -919,8 +919,12 @@ TEST_F(BasicCurlHttpTests, FinishInAsyncCallback)
   }
 }
 
+// Destroying the client wakes the polling background thread instead of letting it sleep out
+// scheduled_delay_milliseconds_. A missed wakeup is slow rather than wrong, so the bound is the
+// assertion: measured, the quit is under a millisecond and a slept out poll is 256 ms.
 TEST_F(BasicCurlHttpTests, ElegantQuitQuick)
 {
+  received_requests_.clear();
   auto http_client = std::make_shared<http_client::curl::HttpCurlClientFactory>()->Create();
   std::static_pointer_cast<curl::HttpClient>(http_client)->MaybeSpawnBackgroundThread();
   // start background first, then test it could wakeup
@@ -929,19 +933,22 @@ TEST_F(BasicCurlHttpTests, ElegantQuitQuick)
   request->SetUri("get/");
   auto handler = std::make_shared<GetEventHandler>();
   session->SendRequest(handler);
-  std::this_thread::sleep_for(std::chrono::milliseconds{10});  // let it enter poll state
+
+  // Sending is not what is timed, so a slow request must not read as a slow quit.
+  ASSERT_TRUE(waitForRequests(30, 1));
+  session->FinishSession();
+  ASSERT_TRUE(handler->is_called_.load(std::memory_order_acquire));
+  ASSERT_TRUE(handler->got_response_.load(std::memory_order_acquire));
+
   auto beg = std::chrono::system_clock::now();
   http_client->FinishAllSessions();
   http_client.reset();
-  // when background_thread_wait_for_ is used, it should have no side effect on elegant quit
-  // wait should be less than scheduled_delay_milliseconds_
-  // Due to load on CI hosts (some take 10ms), we assert it is less than 20ms
   auto cost = std::chrono::system_clock::now() - beg;
-  ASSERT_TRUE(cost < std::chrono::milliseconds{20})
+
+  // background_thread_wait_for_ keeps the thread alive here and must not delay the quit.
+  ASSERT_TRUE(cost < std::chrono::milliseconds{100})
       << "cost ms: " << std::chrono::duration_cast<std::chrono::milliseconds>(cost).count()
       << " libcurl version: 0x" << std::hex << LIBCURL_VERSION_NUM;
-  ASSERT_TRUE(handler->is_called_);
-  ASSERT_TRUE(handler->got_response_);
 }
 
 TEST_F(BasicCurlHttpTests, BackgroundThreadWaitMore)