diff --git a/misc/multistream-select/CHANGELOG.md b/misc/multistream-select/CHANGELOG.md
index b893c5d19e3..670d36dea47 100644
--- a/misc/multistream-select/CHANGELOG.md
+++ b/misc/multistream-select/CHANGELOG.md
@@ -1,8 +1,13 @@
 ## 0.13.0 - unreleased
 
+- Don't wait for negotiation on `<Negotiated as AsyncWrite>::poll_close`.
+  This can save one round-trip for protocols that use stream closing as an operation in ones protocol, e.g. using stream closing to signal the end of a request.
+  See [PR 4019] for details.
+
 - Raise MSRV to 1.65.
   See [PR 3715].
 
+[PR 4019]: https://github.com/libp2p/rust-libp2p/pull/4019
 [PR 3715]: https://github.com/libp2p/rust-libp2p/pull/3715
 
 ## 0.12.1
diff --git a/misc/multistream-select/Cargo.toml b/misc/multistream-select/Cargo.toml
index 100d3c30b7c..b4394812032 100644
--- a/misc/multistream-select/Cargo.toml
+++ b/misc/multistream-select/Cargo.toml
@@ -19,7 +19,7 @@ smallvec = "1.6.1"
 unsigned-varint = "0.7"
 
 [dev-dependencies]
-async-std = "1.6.2"
+async-std = { version = "1.6.2", features = ["attributes"] }
 env_logger = "0.10"
 futures_ringbuf = "0.4.0"
 libp2p-core = { workspace = true }
diff --git a/misc/multistream-select/src/negotiated.rs b/misc/multistream-select/src/negotiated.rs
index dabcec4f605..941b60765ca 100644
--- a/misc/multistream-select/src/negotiated.rs
+++ b/misc/multistream-select/src/negotiated.rs
@@ -305,9 +305,7 @@ where
     }
 
     fn poll_close(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), io::Error>> {
-        // Ensure all data has been flushed and expected negotiation messages
-        // have been received.
-        ready!(self.as_mut().poll(cx).map_err(Into::<io::Error>::into)?);
+        // Ensure all data has been flushed, including optimistic multistream-select messages.
         ready!(self
             .as_mut()
             .poll_flush(cx)
@@ -316,7 +314,13 @@ where
         // Continue with the shutdown of the underlying I/O stream.
         match self.project().state.project() {
             StateProj::Completed { io, .. } => io.poll_close(cx),
-            StateProj::Expecting { io, .. } => io.poll_close(cx),
+            StateProj::Expecting { io, .. } => {
+                let close_poll = io.poll_close(cx);
+                if let Poll::Ready(Ok(())) = close_poll {
+                    log::debug!("Stream closed. Confirmation from remote for optimstic protocol negotiation still pending.")
+                }
+                close_poll
+            }
             StateProj::Invalid => panic!("Negotiated: Invalid state"),
         }
     }
diff --git a/misc/multistream-select/tests/dialer_select.rs b/misc/multistream-select/tests/dialer_select.rs
index 412ccc1a0fd..18f8238cd25 100644
--- a/misc/multistream-select/tests/dialer_select.rs
+++ b/misc/multistream-select/tests/dialer_select.rs
@@ -22,6 +22,7 @@
 
 use futures::prelude::*;
 use multistream_select::{dialer_select_proto, listener_select_proto, NegotiationError, Version};
+use std::time::Duration;
 
 #[test]
 fn select_proto_basic() {
@@ -176,3 +177,26 @@ fn negotiation_failed() {
         }
     }
 }
+
+#[async_std::test]
+async fn v1_lazy_do_not_wait_for_negotiation_on_poll_close() {
+    let (client_connection, _server_connection) = futures_ringbuf::Endpoint::pair(1024 * 1024, 1);
+
+    let client = async_std::task::spawn(async move {
+        // Single protocol to allow for lazy (or optimistic) protocol negotiation.
+        let protos = vec!["/proto1"];
+        let (proto, mut io) =
+            dialer_select_proto(client_connection, protos.into_iter(), Version::V1Lazy)
+                .await
+                .unwrap();
+        assert_eq!(proto, "/proto1");
+
+        // client can close the connection even though protocol negotiation is not yet done, i.e.
+        // `_server_connection` had been untouched.
+        io.close().await.unwrap();
+    });
+
+    async_std::future::timeout(Duration::from_secs(10), client)
+        .await
+        .unwrap();
+}