diff --git a/connectrpc/src/deadline.rs b/connectrpc/src/deadline.rs
index 607af54..e282e1b 100644
--- a/connectrpc/src/deadline.rs
+++ b/connectrpc/src/deadline.rs
@@ -318,7 +318,11 @@ impl<S> DeadlineStream<S> {
         Self {
             inner: Some(inner),
             absolute: absolute.map(tokio::time::sleep),
-            per_item: inter_message.map(tokio::time::sleep),
+            // Do NOT arm the inter-message timer at construction. There is no
+            // prior message yet, so starting the timer here would measure
+            // stream-setup latency rather than the gap between messages. The
+            // lazy arm in `poll_next` starts the timer on the first poll.
+            per_item: None,
             inter_message,
             finished: false,
         }
@@ -337,6 +341,15 @@ where
             return Poll::Ready(None);
         }
 
+        // Lazily arm the inter-message timer on the first poll so that
+        // stream-setup latency before the consumer starts reading is excluded
+        // from the first gap measurement.
+        if this.per_item.is_none() {
+            if let Some(d) = this.inter_message {
+                this.per_item.set(Some(tokio::time::sleep(*d)));
+            }
+        }
+
         // Check the absolute deadline first — once it lapses the whole
         // request is over regardless of per-item progress.
         if let Some(sleep) = this.absolute.as_mut().as_pin_mut()
@@ -589,4 +602,36 @@ mod tests {
         );
         assert!(wrapped.next().await.is_none());
     }
+
+    #[tokio::test(start_paused = true)]
+    async fn setup_latency_before_first_poll_does_not_trigger_timeout() {
+        let p = DeadlinePolicy::new().with_inter_message_timeout(ms(50));
+        let inner: BoxStream<Result<Bytes, ConnectError>> =
+            Box::pin(futures::stream::iter([Ok(Bytes::from_static(b"a"))]));
+        let mut wrapped = p.enforce_on_response_stream(inner, None);
+
+        tokio::time::advance(ms(100)).await;
+
+        let item = wrapped.next().await.unwrap();
+        assert!(item.is_ok(), "expected first item but got deadline error: {:?}", item);
+        assert_eq!(item.unwrap(), Bytes::from_static(b"a"));
+    }
+
+    #[tokio::test(start_paused = true)]
+    async fn stream_that_never_yields_still_times_out() {
+        let p = DeadlinePolicy::new().with_inter_message_timeout(ms(50));
+        let inner: BoxStream<Result<Bytes, ConnectError>> =
+            Box::pin(futures::stream::pending());
+        let mut wrapped = p.enforce_on_response_stream(inner, None);
+
+        let first = futures::poll!(wrapped.next());
+        assert!(first.is_pending());
+
+        tokio::time::advance(ms(100)).await;
+
+        let err = wrapped.next().await.unwrap().unwrap_err();
+        assert_eq!(err.code, crate::ErrorCode::DeadlineExceeded);
+        assert!(err.message.as_deref().unwrap().contains("inter-message"));
+        assert!(wrapped.next().await.is_none());
+    }
 }