diff --git a/core/CHANGELOG.md b/core/CHANGELOG.md
index 047a7ac4..dc4fd082 100644
--- a/core/CHANGELOG.md
+++ b/core/CHANGELOG.md
@@ -4,11 +4,13 @@
   and `poll_address_change`. Consequently, `StreamMuxerEvent` is also removed. See [PR 2724].
 - Drop `Unpin` requirement from `SubstreamBox`. See [PR 2762] and [PR 2776].
 - Drop `Sync` requirement on `StreamMuxer` for constructing `StreamMuxerBox`. See [PR 2775].
+- Use `Pin<&mut Self>` as the receiver type for all `StreamMuxer` poll functions. See [PR 2765].
 
 [PR 2724]: https://github.com/libp2p/rust-libp2p/pull/2724
 [PR 2762]: https://github.com/libp2p/rust-libp2p/pull/2762
 [PR 2775]: https://github.com/libp2p/rust-libp2p/pull/2775
 [PR 2776]: https://github.com/libp2p/rust-libp2p/pull/2776
+[PR 2765]: https://github.com/libp2p/rust-libp2p/pull/2765
 
 # 0.34.0
 
diff --git a/core/src/either.rs b/core/src/either.rs
index 4b5c20b2..42984519 100644
--- a/core/src/either.rs
+++ b/core/src/either.rs
@@ -204,43 +204,54 @@ where
     type Substream = EitherOutput<A::Substream, B::Substream>;
     type Error = EitherError<A::Error, B::Error>;
 
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        match self {
-            EitherOutput::First(inner) => inner
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        match self.project() {
+            EitherOutputProj::First(inner) => inner
                 .poll_inbound(cx)
                 .map_ok(EitherOutput::First)
                 .map_err(EitherError::A),
-            EitherOutput::Second(inner) => inner
+            EitherOutputProj::Second(inner) => inner
                 .poll_inbound(cx)
                 .map_ok(EitherOutput::Second)
                 .map_err(EitherError::B),
         }
     }
 
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        match self {
-            EitherOutput::First(inner) => inner
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        match self.project() {
+            EitherOutputProj::First(inner) => inner
                 .poll_outbound(cx)
                 .map_ok(EitherOutput::First)
                 .map_err(EitherError::A),
-            EitherOutput::Second(inner) => inner
+            EitherOutputProj::Second(inner) => inner
                 .poll_outbound(cx)
                 .map_ok(EitherOutput::Second)
                 .map_err(EitherError::B),
         }
     }
 
-    fn poll_address_change(&self, cx: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
-        match self {
-            EitherOutput::First(inner) => inner.poll_address_change(cx).map_err(EitherError::A),
-            EitherOutput::Second(inner) => inner.poll_address_change(cx).map_err(EitherError::B),
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
+        match self.project() {
+            EitherOutputProj::First(inner) => inner.poll_address_change(cx).map_err(EitherError::A),
+            EitherOutputProj::Second(inner) => {
+                inner.poll_address_change(cx).map_err(EitherError::B)
+            }
         }
     }
 
-    fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
-        match self {
-            EitherOutput::First(inner) => inner.poll_close(cx).map_err(EitherError::A),
-            EitherOutput::Second(inner) => inner.poll_close(cx).map_err(EitherError::B),
+    fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
+        match self.project() {
+            EitherOutputProj::First(inner) => inner.poll_close(cx).map_err(EitherError::A),
+            EitherOutputProj::Second(inner) => inner.poll_close(cx).map_err(EitherError::B),
         }
     }
 }
diff --git a/core/src/muxing.rs b/core/src/muxing.rs
index a2bdfa80..2d1e1068 100644
--- a/core/src/muxing.rs
+++ b/core/src/muxing.rs
@@ -52,6 +52,8 @@
 
 use futures::{task::Context, task::Poll, AsyncRead, AsyncWrite};
 use multiaddr::Multiaddr;
+use std::future::Future;
+use std::pin::Pin;
 
 pub use self::boxed::StreamMuxerBox;
 pub use self::boxed::SubstreamBox;
@@ -73,15 +75,24 @@ pub trait StreamMuxer {
     type Error: std::error::Error;
 
     /// Poll for new inbound substreams.
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>>;
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>>;
 
     /// Poll for a new, outbound substream.
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>>;
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>>;
 
     /// Poll for an address change of the underlying connection.
     ///
     /// Not all implementations may support this feature.
-    fn poll_address_change(&self, cx: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>>;
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>>;
 
     /// Closes this `StreamMuxer`.
     ///
@@ -93,5 +104,105 @@ pub trait StreamMuxer {
     /// >           that the remote is properly informed of the shutdown. However, apart from
     /// >           properly informing the remote, there is no difference between this and
     /// >           immediately dropping the muxer.
-    fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>>;
+    fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>>;
+}
+
+/// Extension trait for [`StreamMuxer`].
+pub trait StreamMuxerExt: StreamMuxer + Sized {
+    /// Convenience function for calling [`StreamMuxer::poll_inbound`] for [`StreamMuxer`]s that are `Unpin`.
+    fn poll_inbound_unpin(
+        &mut self,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>>
+    where
+        Self: Unpin,
+    {
+        Pin::new(self).poll_inbound(cx)
+    }
+
+    /// Convenience function for calling [`StreamMuxer::poll_outbound`] for [`StreamMuxer`]s that are `Unpin`.
+    fn poll_outbound_unpin(
+        &mut self,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>>
+    where
+        Self: Unpin,
+    {
+        Pin::new(self).poll_outbound(cx)
+    }
+
+    /// Convenience function for calling [`StreamMuxer::poll_address_change`] for [`StreamMuxer`]s that are `Unpin`.
+    fn poll_address_change_unpin(
+        &mut self,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>>
+    where
+        Self: Unpin,
+    {
+        Pin::new(self).poll_address_change(cx)
+    }
+
+    /// Convenience function for calling [`StreamMuxer::poll_close`] for [`StreamMuxer`]s that are `Unpin`.
+    fn poll_close_unpin(&mut self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>>
+    where
+        Self: Unpin,
+    {
+        Pin::new(self).poll_close(cx)
+    }
+
+    /// Returns a future that resolves to the next inbound `Substream` opened by the remote.
+    fn next_inbound(&mut self) -> NextInbound<'_, Self> {
+        NextInbound(self)
+    }
+
+    /// Returns a future that opens a new outbound `Substream` with the remote.
+    fn next_outbound(&mut self) -> NextOutbound<'_, Self> {
+        NextOutbound(self)
+    }
+
+    /// Returns a future for closing this [`StreamMuxer`].
+    fn close(self) -> Close<Self> {
+        Close(self)
+    }
+}
+
+impl<S> StreamMuxerExt for S where S: StreamMuxer {}
+
+pub struct NextInbound<'a, S>(&'a mut S);
+
+pub struct NextOutbound<'a, S>(&'a mut S);
+
+pub struct Close<S>(S);
+
+impl<'a, S> Future for NextInbound<'a, S>
+where
+    S: StreamMuxer + Unpin,
+{
+    type Output = Result<S::Substream, S::Error>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        self.0.poll_inbound_unpin(cx)
+    }
+}
+
+impl<'a, S> Future for NextOutbound<'a, S>
+where
+    S: StreamMuxer + Unpin,
+{
+    type Output = Result<S::Substream, S::Error>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        self.0.poll_outbound_unpin(cx)
+    }
+}
+
+impl<S> Future for Close<S>
+where
+    S: StreamMuxer + Unpin,
+{
+    type Output = Result<(), S::Error>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        self.0.poll_close_unpin(cx)
+    }
 }
diff --git a/core/src/muxing/boxed.rs b/core/src/muxing/boxed.rs
index 8c6467dd..0f5b6e58 100644
--- a/core/src/muxing/boxed.rs
+++ b/core/src/muxing/boxed.rs
@@ -1,6 +1,7 @@
 use crate::StreamMuxer;
 use futures::{AsyncRead, AsyncWrite};
 use multiaddr::Multiaddr;
+use pin_project::pin_project;
 use std::error::Error;
 use std::fmt;
 use std::io;
@@ -10,7 +11,7 @@ use std::task::{Context, Poll};
 
 /// Abstract `StreamMuxer`.
 pub struct StreamMuxerBox {
-    inner: Box<dyn StreamMuxer<Substream = SubstreamBox, Error = io::Error> + Send>,
+    inner: Pin<Box<dyn StreamMuxer<Substream = SubstreamBox, Error = io::Error> + Send>>,
 }
 
 /// Abstract type for asynchronous reading and writing.
@@ -19,10 +20,12 @@ pub struct StreamMuxerBox {
 /// and `AsyncWrite` capabilities.
 pub struct SubstreamBox(Pin<Box<dyn AsyncReadWrite + Send>>);
 
+#[pin_project]
 struct Wrap<T>
 where
     T: StreamMuxer,
 {
+    #[pin]
     inner: T,
 }
 
@@ -36,26 +39,40 @@ where
     type Error = io::Error;
 
     #[inline]
-    fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
-        self.inner.poll_close(cx).map_err(into_io_error)
+    fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
+        self.project().inner.poll_close(cx).map_err(into_io_error)
     }
 
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        self.inner
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        self.project()
+            .inner
             .poll_inbound(cx)
             .map_ok(SubstreamBox::new)
             .map_err(into_io_error)
     }
 
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        self.inner
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        self.project()
+            .inner
             .poll_outbound(cx)
             .map_ok(SubstreamBox::new)
             .map_err(into_io_error)
     }
 
-    fn poll_address_change(&self, cx: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
-        self.inner.poll_address_change(cx).map_err(into_io_error)
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
+        self.project()
+            .inner
+            .poll_address_change(cx)
+            .map_err(into_io_error)
     }
 }
 
@@ -77,9 +94,15 @@ impl StreamMuxerBox {
         let wrap = Wrap { inner: muxer };
 
         StreamMuxerBox {
-            inner: Box::new(wrap),
+            inner: Box::pin(wrap),
         }
     }
+
+    fn project(
+        self: Pin<&mut Self>,
+    ) -> Pin<&mut (dyn StreamMuxer<Substream = SubstreamBox, Error = io::Error> + Send)> {
+        self.get_mut().inner.as_mut()
+    }
 }
 
 impl StreamMuxer for StreamMuxerBox {
@@ -87,20 +110,29 @@ impl StreamMuxer for StreamMuxerBox {
     type Error = io::Error;
 
     #[inline]
-    fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
-        self.inner.poll_close(cx)
+    fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
+        self.project().poll_close(cx)
     }
 
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        self.inner.poll_inbound(cx)
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        self.project().poll_inbound(cx)
     }
 
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        self.inner.poll_outbound(cx)
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        self.project().poll_outbound(cx)
     }
 
-    fn poll_address_change(&self, cx: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
-        self.inner.poll_address_change(cx)
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
+        self.project().poll_address_change(cx)
     }
 }
 
diff --git a/core/src/muxing/singleton.rs b/core/src/muxing/singleton.rs
index d67cb5e9..193cfb63 100644
--- a/core/src/muxing/singleton.rs
+++ b/core/src/muxing/singleton.rs
@@ -23,6 +23,7 @@ use crate::{connection::Endpoint, muxing::StreamMuxer};
 use futures::prelude::*;
 use multiaddr::Multiaddr;
 use std::cell::Cell;
+use std::pin::Pin;
 use std::{io, task::Context, task::Poll};
 
 /// Implementation of `StreamMuxer` that allows only one substream on top of a connection,
@@ -57,31 +58,44 @@ where
     type Substream = TSocket;
     type Error = io::Error;
 
-    fn poll_inbound(&self, _: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        match self.endpoint {
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        _: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        let this = self.get_mut();
+
+        match this.endpoint {
             Endpoint::Dialer => Poll::Pending,
-            Endpoint::Listener => match self.inner.replace(None) {
+            Endpoint::Listener => match this.inner.replace(None) {
                 None => Poll::Pending,
                 Some(stream) => Poll::Ready(Ok(stream)),
             },
         }
     }
 
-    fn poll_outbound(&self, _: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        match self.endpoint {
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        _: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        let this = self.get_mut();
+
+        match this.endpoint {
             Endpoint::Listener => Poll::Pending,
-            Endpoint::Dialer => match self.inner.replace(None) {
+            Endpoint::Dialer => match this.inner.replace(None) {
                 None => Poll::Pending,
                 Some(stream) => Poll::Ready(Ok(stream)),
             },
         }
     }
 
-    fn poll_address_change(&self, _: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        _: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
         Poll::Pending
     }
 
-    fn poll_close(&self, _cx: &mut Context<'_>) -> Poll<Result<(), io::Error>> {
+    fn poll_close(self: Pin<&mut Self>, _cx: &mut Context<'_>) -> Poll<Result<(), io::Error>> {
         Poll::Ready(Ok(()))
     }
 }
diff --git a/muxers/mplex/benches/split_send_size.rs b/muxers/mplex/benches/split_send_size.rs
index d536edf4..f74bcd10 100644
--- a/muxers/mplex/benches/split_send_size.rs
+++ b/muxers/mplex/benches/split_send_size.rs
@@ -26,9 +26,9 @@ use criterion::{black_box, criterion_group, criterion_main, Criterion, Throughpu
 use futures::future::poll_fn;
 use futures::prelude::*;
 use futures::{channel::oneshot, future::join};
+use libp2p_core::muxing::StreamMuxerExt;
 use libp2p_core::{
-    identity, multiaddr::multiaddr, muxing, transport, upgrade, Multiaddr, PeerId, StreamMuxer,
-    Transport,
+    identity, multiaddr::multiaddr, muxing, transport, upgrade, Multiaddr, PeerId, Transport,
 };
 use libp2p_mplex as mplex;
 use libp2p_plaintext::PlainText2Config;
@@ -113,10 +113,8 @@ fn run(
                     addr_sender.take().unwrap().send(listen_addr).unwrap();
                 }
                 transport::TransportEvent::Incoming { upgrade, .. } => {
-                    let (_peer, conn) = upgrade.await.unwrap();
-                    let mut s = poll_fn(|cx| conn.poll_inbound(cx))
-                        .await
-                        .expect("unexpected error");
+                    let (_peer, mut conn) = upgrade.await.unwrap();
+                    let mut s = conn.next_inbound().await.expect("unexpected error");
 
                     let mut buf = vec![0u8; payload_len];
                     let mut off = 0;
@@ -140,8 +138,8 @@ fn run(
     // Spawn and block on the sender, i.e. until all data is sent.
     let sender = async move {
         let addr = addr_receiver.await.unwrap();
-        let (_peer, conn) = sender_trans.dial(addr).unwrap().await.unwrap();
-        let mut stream = poll_fn(|cx| conn.poll_outbound(cx)).await.unwrap();
+        let (_peer, mut conn) = sender_trans.dial(addr).unwrap().await.unwrap();
+        let mut stream = conn.next_outbound().await.unwrap();
         let mut off = 0;
         loop {
             let n = poll_fn(|cx| Pin::new(&mut stream).poll_write(cx, &payload[off..]))
diff --git a/muxers/mplex/src/lib.rs b/muxers/mplex/src/lib.rs
index 59b38db1..14f9cda6 100644
--- a/muxers/mplex/src/lib.rs
+++ b/muxers/mplex/src/lib.rs
@@ -85,25 +85,34 @@ where
     type Substream = Substream<C>;
     type Error = io::Error;
 
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
+    fn poll_inbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
         self.io
             .lock()
             .poll_next_stream(cx)
             .map_ok(|stream_id| Substream::new(stream_id, self.io.clone()))
     }
 
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
+    fn poll_outbound(
+        self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
         self.io
             .lock()
             .poll_open_stream(cx)
             .map_ok(|stream_id| Substream::new(stream_id, self.io.clone()))
     }
 
-    fn poll_address_change(&self, _: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        _: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
         Poll::Pending
     }
 
-    fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), io::Error>> {
+    fn poll_close(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Result<(), io::Error>> {
         self.io.lock().poll_close(cx)
     }
 }
diff --git a/muxers/mplex/tests/async_write.rs b/muxers/mplex/tests/async_write.rs
index 2c4a2d10..bfbabf0f 100644
--- a/muxers/mplex/tests/async_write.rs
+++ b/muxers/mplex/tests/async_write.rs
@@ -18,9 +18,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 // DEALINGS IN THE SOFTWARE.
 
-use futures::future::poll_fn;
 use futures::{channel::oneshot, prelude::*};
-use libp2p_core::{upgrade, StreamMuxer, Transport};
+use libp2p_core::muxing::StreamMuxerExt;
+use libp2p_core::{upgrade, Transport};
 use libp2p_tcp::TcpTransport;
 
 #[test]
@@ -49,7 +49,7 @@ fn async_write() {
 
         tx.send(addr).unwrap();
 
-        let client = transport
+        let mut client = transport
             .next()
             .await
             .expect("some event")
@@ -59,7 +59,7 @@ fn async_write() {
             .await
             .unwrap();
 
-        let mut outbound = poll_fn(|cx| client.poll_outbound(cx)).await.unwrap();
+        let mut outbound = client.next_outbound().await.unwrap();
 
         let mut buf = Vec::new();
         outbound.read_to_end(&mut buf).await.unwrap();
@@ -71,8 +71,9 @@ fn async_write() {
         let mut transport = TcpTransport::default()
             .and_then(move |c, e| upgrade::apply(c, mplex, e, upgrade::Version::V1));
 
-        let client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
-        let mut inbound = poll_fn(|cx| client.poll_inbound(cx)).await.unwrap();
+        let mut client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
+
+        let mut inbound = client.next_inbound().await.unwrap();
         inbound.write_all(b"hello world").await.unwrap();
 
         // The test consists in making sure that this flushes the substream.
diff --git a/muxers/mplex/tests/two_peers.rs b/muxers/mplex/tests/two_peers.rs
index 2b976c12..d30fcc10 100644
--- a/muxers/mplex/tests/two_peers.rs
+++ b/muxers/mplex/tests/two_peers.rs
@@ -18,9 +18,9 @@
 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 // DEALINGS IN THE SOFTWARE.
 
-use futures::future::poll_fn;
 use futures::{channel::oneshot, prelude::*};
-use libp2p_core::{upgrade, StreamMuxer, Transport};
+use libp2p_core::muxing::StreamMuxerExt;
+use libp2p_core::{upgrade, Transport};
 use libp2p_tcp::TcpTransport;
 
 #[test]
@@ -49,7 +49,7 @@ fn client_to_server_outbound() {
 
         tx.send(addr).unwrap();
 
-        let client = transport
+        let mut client = transport
             .next()
             .await
             .expect("some event")
@@ -59,7 +59,7 @@ fn client_to_server_outbound() {
             .await
             .unwrap();
 
-        let mut outbound = poll_fn(|cx| client.poll_outbound(cx)).await.unwrap();
+        let mut outbound = client.next_outbound().await.unwrap();
 
         let mut buf = Vec::new();
         outbound.read_to_end(&mut buf).await.unwrap();
@@ -72,8 +72,8 @@ fn client_to_server_outbound() {
             .and_then(move |c, e| upgrade::apply(c, mplex, e, upgrade::Version::V1))
             .boxed();
 
-        let client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
-        let mut inbound = poll_fn(|cx| client.poll_inbound(cx)).await.unwrap();
+        let mut client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
+        let mut inbound = client.next_inbound().await.unwrap();
         inbound.write_all(b"hello world").await.unwrap();
         inbound.close().await.unwrap();
 
@@ -107,7 +107,7 @@ fn client_to_server_inbound() {
 
         tx.send(addr).unwrap();
 
-        let client = transport
+        let mut client = transport
             .next()
             .await
             .expect("some event")
@@ -117,7 +117,7 @@ fn client_to_server_inbound() {
             .await
             .unwrap();
 
-        let mut inbound = poll_fn(|cx| client.poll_inbound(cx)).await.unwrap();
+        let mut inbound = client.next_inbound().await.unwrap();
 
         let mut buf = Vec::new();
         inbound.read_to_end(&mut buf).await.unwrap();
@@ -130,9 +130,9 @@ fn client_to_server_inbound() {
             .and_then(move |c, e| upgrade::apply(c, mplex, e, upgrade::Version::V1))
             .boxed();
 
-        let client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
+        let mut client = transport.dial(rx.await.unwrap()).unwrap().await.unwrap();
 
-        let mut outbound = poll_fn(|cx| client.poll_outbound(cx)).await.unwrap();
+        let mut outbound = client.next_outbound().await.unwrap();
         outbound.write_all(b"hello world").await.unwrap();
         outbound.close().await.unwrap();
 
@@ -164,7 +164,7 @@ fn protocol_not_match() {
 
         tx.send(addr).unwrap();
 
-        let client = transport
+        let mut client = transport
             .next()
             .await
             .expect("some event")
@@ -174,7 +174,7 @@ fn protocol_not_match() {
             .await
             .unwrap();
 
-        let mut outbound = poll_fn(|cx| client.poll_outbound(cx)).await.unwrap();
+        let mut outbound = client.next_outbound().await.unwrap();
 
         let mut buf = Vec::new();
         outbound.read_to_end(&mut buf).await.unwrap();
diff --git a/muxers/yamux/src/lib.rs b/muxers/yamux/src/lib.rs
index a06e7934..07327e20 100644
--- a/muxers/yamux/src/lib.rs
+++ b/muxers/yamux/src/lib.rs
@@ -29,7 +29,6 @@ use futures::{
 use libp2p_core::muxing::StreamMuxer;
 use libp2p_core::upgrade::{InboundUpgrade, OutboundUpgrade, UpgradeInfo};
 use libp2p_core::Multiaddr;
-use parking_lot::Mutex;
 use std::{
     fmt, io, iter, mem,
     pin::Pin,
@@ -39,7 +38,12 @@ use thiserror::Error;
 use yamux::ConnectionError;
 
 /// A Yamux connection.
-pub struct Yamux<S>(Mutex<Inner<S>>);
+pub struct Yamux<S> {
+    /// The [`futures::stream::Stream`] of incoming substreams.
+    incoming: S,
+    /// Handle to control the connection.
+    control: yamux::Control,
+}
 
 impl<S> fmt::Debug for Yamux<S> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
@@ -47,13 +51,6 @@ impl<S> fmt::Debug for Yamux<S> {
     }
 }
 
-struct Inner<S> {
-    /// The [`futures::stream::Stream`] of incoming substreams.
-    incoming: S,
-    /// Handle to control the connection.
-    control: yamux::Control,
-}
-
 /// A token to poll for an outbound substream.
 #[derive(Debug)]
 pub struct OpenSubstreamToken(());
@@ -66,14 +63,14 @@ where
     fn new(io: C, cfg: yamux::Config, mode: yamux::Mode) -> Self {
         let conn = yamux::Connection::new(io, cfg, mode);
         let ctrl = conn.control();
-        let inner = Inner {
+
+        Yamux {
             incoming: Incoming {
                 stream: yamux::into_stream(conn).err_into().boxed(),
                 _marker: std::marker::PhantomData,
             },
             control: ctrl,
-        };
-        Yamux(Mutex::new(inner))
+        }
     }
 }
 
@@ -85,14 +82,14 @@ where
     fn local(io: C, cfg: yamux::Config, mode: yamux::Mode) -> Self {
         let conn = yamux::Connection::new(io, cfg, mode);
         let ctrl = conn.control();
-        let inner = Inner {
+
+        Yamux {
             incoming: LocalIncoming {
                 stream: yamux::into_stream(conn).err_into().boxed_local(),
                 _marker: std::marker::PhantomData,
             },
             control: ctrl,
-        };
-        Yamux(Mutex::new(inner))
+        }
     }
 }
 
@@ -105,41 +102,44 @@ where
     type Substream = yamux::Stream;
     type Error = YamuxError;
 
-    fn poll_inbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        self.0
-            .lock()
-            .incoming
-            .poll_next_unpin(cx)
-            .map(|maybe_stream| {
-                let stream = maybe_stream
-                    .transpose()?
-                    .ok_or(YamuxError(ConnectionError::Closed))?;
+    fn poll_inbound(
+        mut self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        self.incoming.poll_next_unpin(cx).map(|maybe_stream| {
+            let stream = maybe_stream
+                .transpose()?
+                .ok_or(YamuxError(ConnectionError::Closed))?;
 
-                Ok(stream)
-            })
+            Ok(stream)
+        })
     }
 
-    fn poll_outbound(&self, cx: &mut Context<'_>) -> Poll<Result<Self::Substream, Self::Error>> {
-        Pin::new(&mut self.0.lock().control)
+    fn poll_outbound(
+        mut self: Pin<&mut Self>,
+        cx: &mut Context<'_>,
+    ) -> Poll<Result<Self::Substream, Self::Error>> {
+        Pin::new(&mut self.control)
             .poll_open_stream(cx)
             .map_err(YamuxError)
     }
 
-    fn poll_address_change(&self, _: &mut Context<'_>) -> Poll<Result<Multiaddr, Self::Error>> {
+    fn poll_address_change(
+        self: Pin<&mut Self>,
+        _: &mut Context<'_>,
+    ) -> Poll<Result<Multiaddr, Self::Error>> {
         Poll::Pending
     }
 
-    fn poll_close(&self, c: &mut Context<'_>) -> Poll<YamuxResult<()>> {
-        let mut inner = self.0.lock();
-
-        if let Poll::Ready(()) = Pin::new(&mut inner.control)
+    fn poll_close(mut self: Pin<&mut Self>, c: &mut Context<'_>) -> Poll<YamuxResult<()>> {
+        if let Poll::Ready(()) = Pin::new(&mut self.control)
             .poll_close(c)
             .map_err(YamuxError)?
         {
             return Poll::Ready(Ok(()));
         }
 
-        while let Poll::Ready(maybe_inbound_stream) = inner.incoming.poll_next_unpin(c)? {
+        while let Poll::Ready(maybe_inbound_stream) = self.incoming.poll_next_unpin(c)? {
             match maybe_inbound_stream {
                 Some(inbound_stream) => mem::drop(inbound_stream),
                 None => return Poll::Ready(Ok(())),
diff --git a/swarm/src/connection.rs b/swarm/src/connection.rs
index 8d29ca53..f9218661 100644
--- a/swarm/src/connection.rs
+++ b/swarm/src/connection.rs
@@ -32,13 +32,12 @@ pub use pool::{EstablishedConnection, PendingConnection};
 
 use crate::handler::ConnectionHandler;
 use crate::IntoConnectionHandler;
-use futures::future::poll_fn;
 use handler_wrapper::HandlerWrapper;
 use libp2p_core::connection::ConnectedPoint;
 use libp2p_core::multiaddr::Multiaddr;
-use libp2p_core::muxing::StreamMuxerBox;
+use libp2p_core::muxing::{StreamMuxerBox, StreamMuxerExt};
+use libp2p_core::upgrade;
 use libp2p_core::PeerId;
-use libp2p_core::{upgrade, StreamMuxer};
 use std::collections::VecDeque;
 use std::future::Future;
 use std::{error::Error, fmt, io, pin::Pin, task::Context, task::Poll};
@@ -132,10 +131,7 @@ where
     /// Begins an orderly shutdown of the connection, returning the connection
     /// handler and a `Future` that resolves when connection shutdown is complete.
     pub fn close(self) -> (THandler, impl Future<Output = io::Result<()>>) {
-        (
-            self.handler.into_connection_handler(),
-            poll_fn(move |cx| self.muxing.poll_close(cx)),
-        )
+        (self.handler.into_connection_handler(), self.muxing.close())
     }
 
     /// Polls the handler and the substream, forwarding events from the former to the latter and
@@ -158,7 +154,7 @@ where
             }
 
             if !self.open_info.is_empty() {
-                if let Poll::Ready(substream) = self.muxing.poll_outbound(cx)? {
+                if let Poll::Ready(substream) = self.muxing.poll_outbound_unpin(cx)? {
                     let user_data = self
                         .open_info
                         .pop_front()
@@ -169,13 +165,13 @@ where
                 }
             }
 
-            if let Poll::Ready(substream) = self.muxing.poll_inbound(cx)? {
+            if let Poll::Ready(substream) = self.muxing.poll_inbound_unpin(cx)? {
                 self.handler
                     .inject_substream(substream, SubstreamEndpoint::Listener);
                 continue; // Go back to the top, handler can potentially make progress again.
             }
 
-            if let Poll::Ready(address) = self.muxing.poll_address_change(cx)? {
+            if let Poll::Ready(address) = self.muxing.poll_address_change_unpin(cx)? {
                 self.handler.inject_address_change(&address);
                 return Poll::Ready(Ok(Event::AddressChange(address)));
             }
diff --git a/swarm/src/connection/pool.rs b/swarm/src/connection/pool.rs
index 4bbdf9c4..62e931e9 100644
--- a/swarm/src/connection/pool.rs
+++ b/swarm/src/connection/pool.rs
@@ -38,7 +38,7 @@ use futures::{
     stream::FuturesUnordered,
 };
 use libp2p_core::connection::{ConnectionId, Endpoint, PendingPoint};
-use libp2p_core::muxing::{StreamMuxer, StreamMuxerBox};
+use libp2p_core::muxing::{StreamMuxerBox, StreamMuxerExt};
 use std::{
     collections::{hash_map, HashMap},
     convert::TryFrom as _,
@@ -604,7 +604,7 @@ where
             match event {
                 task::PendingConnectionEvent::ConnectionEstablished {
                     id,
-                    output: (obtained_peer_id, muxer),
+                    output: (obtained_peer_id, mut muxer),
                     outgoing,
                 } => {
                     let PendingConnectionInfo {
@@ -692,7 +692,7 @@ where
                     if let Err(error) = error {
                         self.spawn(
                             poll_fn(move |cx| {
-                                if let Err(e) = ready!(muxer.poll_close(cx)) {
+                                if let Err(e) = ready!(muxer.poll_close_unpin(cx)) {
                                     log::debug!(
                                         "Failed to close connection {:?} to peer {}: {:?}",
                                         id,