diff --git a/codex-rs/core/tests/common/responses.rs b/codex-rs/core/tests/common/responses.rs
index c917436b6d..6c3ed0ef44 100644
--- a/codex-rs/core/tests/common/responses.rs
+++ b/codex-rs/core/tests/common/responses.rs
@@ -1246,7 +1246,10 @@ pub async fn start_websocket_server_with_headers(
             };
 
             if let Some(delay) = connection.accept_delay {
-                tokio::time::sleep(delay).await;
+                tokio::select! {
+                    _ = &mut shutdown_rx => return,
+                    _ = tokio::time::sleep(delay) => {}
+                }
             }
 
             let response_headers = connection.response_headers.clone();
diff --git a/codex-rs/core/tests/suite/realtime_conversation.rs b/codex-rs/core/tests/suite/realtime_conversation.rs
index 4be7eae2d7..12f19be8d0 100644
--- a/codex-rs/core/tests/suite/realtime_conversation.rs
+++ b/codex-rs/core/tests/suite/realtime_conversation.rs
@@ -649,8 +649,8 @@ async fn conversation_webrtc_start_posts_generated_session() -> Result<()> {
 async fn conversation_webrtc_close_while_sideband_connecting_drops_pending_join() -> Result<()> {
     skip_if_no_network!(Ok(()));
 
-    let sideband_accept_delay = Duration::from_millis(700);
-    let stale_sideband_observation_window = Duration::from_secs(1);
+    let sideband_accept_delay = Duration::from_secs(5);
+    let stale_sideband_observation_window = Duration::from_millis(700);
     let server = start_mock_server().await;
     Mock::given(method("POST"))
         .and(path_regex(".*/realtime/calls$"))
@@ -664,8 +664,8 @@ async fn conversation_webrtc_close_while_sideband_connecting_drops_pending_join(
     let realtime_server = start_websocket_server_with_headers(vec![WebSocketConnectionConfig {
         requests: vec![vec![]],
         response_headers: Vec::new(),
-        // Keep the sideband handshake pending through the close path on slow CI without adding a
-        // multi-second fixed tail when the mock websocket server shuts down.
+        // Keep the sideband handshake pending beyond the stale-event observation window below
+        // without adding a multi-second fixed tail when the mock websocket server shuts down.
         accept_delay: Some(sideband_accept_delay),
         close_after_requests: false,
     }])