diff --git a/core/CHANGELOG.md b/core/CHANGELOG.md
index b89683c3a01..7bea0f3f35a 100644
--- a/core/CHANGELOG.md
+++ b/core/CHANGELOG.md
@@ -3,9 +3,11 @@
 - Introduce `StreamMuxerEvent::map_inbound_stream`. See [PR 2691].
 - Remove `{read,write,flush,shutdown,destroy}_substream` functions from `StreamMuxer` trait
   in favor of forcing `StreamMuxer::Substream` to implement `AsyncRead + AsyncWrite`. See [PR 2707].
+- Replace `Into<std::io::Error>` bound on `StreamMuxer::Error` with `std::error::Error`. See [PR 2710].
 
 [PR 2691]: https://github.com/libp2p/rust-libp2p/pull/2691
 [PR 2707]: https://github.com/libp2p/rust-libp2p/pull/2707
+[PR 2710]: https://github.com/libp2p/rust-libp2p/pull/2710
 
 # 0.33.0
 
diff --git a/core/src/either.rs b/core/src/either.rs
index 55b616d78a6..8ce9046f6f8 100644
--- a/core/src/either.rs
+++ b/core/src/either.rs
@@ -203,7 +203,7 @@ where
 {
     type Substream = EitherOutput<A::Substream, B::Substream>;
     type OutboundSubstream = EitherOutbound<A, B>;
-    type Error = io::Error;
+    type Error = EitherError<A::Error, B::Error>;
 
     fn poll_event(
         &self,
@@ -212,11 +212,11 @@ where
         match self {
             EitherOutput::First(inner) => inner
                 .poll_event(cx)
-                .map_err(|e| e.into())
+                .map_err(EitherError::A)
                 .map_ok(|event| event.map_inbound_stream(EitherOutput::First)),
             EitherOutput::Second(inner) => inner
                 .poll_event(cx)
-                .map_err(|e| e.into())
+                .map_err(EitherError::B)
                 .map_ok(|event| event.map_inbound_stream(EitherOutput::Second)),
         }
     }
@@ -237,11 +237,11 @@ where
             (EitherOutput::First(ref inner), EitherOutbound::A(ref mut substream)) => inner
                 .poll_outbound(cx, substream)
                 .map(|p| p.map(EitherOutput::First))
-                .map_err(|e| e.into()),
+                .map_err(EitherError::A),
             (EitherOutput::Second(ref inner), EitherOutbound::B(ref mut substream)) => inner
                 .poll_outbound(cx, substream)
                 .map(|p| p.map(EitherOutput::Second))
-                .map_err(|e| e.into()),
+                .map_err(EitherError::B),
             _ => panic!("Wrong API usage"),
         }
     }
@@ -261,8 +261,8 @@ where
 
     fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
         match self {
-            EitherOutput::First(inner) => inner.poll_close(cx).map_err(|e| e.into()),
-            EitherOutput::Second(inner) => inner.poll_close(cx).map_err(|e| e.into()),
+            EitherOutput::First(inner) => inner.poll_close(cx).map_err(EitherError::A),
+            EitherOutput::Second(inner) => inner.poll_close(cx).map_err(EitherError::B),
         }
     }
 }
diff --git a/core/src/muxing.rs b/core/src/muxing.rs
index 68e555e167f..050d8d1bd35 100644
--- a/core/src/muxing.rs
+++ b/core/src/muxing.rs
@@ -52,7 +52,6 @@
 
 use futures::{task::Context, task::Poll, AsyncRead, AsyncWrite};
 use multiaddr::Multiaddr;
-use std::io;
 
 pub use self::boxed::StreamMuxerBox;
 pub use self::boxed::SubstreamBox;
@@ -76,7 +75,7 @@ pub trait StreamMuxer {
     type OutboundSubstream;
 
     /// Error type of the muxer
-    type Error: Into<io::Error>;
+    type Error: std::error::Error;
 
     /// Polls for a connection-wide event.
     ///
diff --git a/core/src/muxing/boxed.rs b/core/src/muxing/boxed.rs
index f0e2ff10647..ad39ef0532d 100644
--- a/core/src/muxing/boxed.rs
+++ b/core/src/muxing/boxed.rs
@@ -1,8 +1,9 @@
 use crate::muxing::StreamMuxerEvent;
 use crate::StreamMuxer;
 use fnv::FnvHashMap;
-use futures::{AsyncRead, AsyncWrite};
+use futures::{ready, AsyncRead, AsyncWrite};
 use parking_lot::Mutex;
+use std::error::Error;
 use std::fmt;
 use std::io;
 use std::io::{IoSlice, IoSliceMut};
@@ -38,6 +39,7 @@ impl<T> StreamMuxer for Wrap<T>
 where
     T: StreamMuxer,
     T::Substream: Send + Unpin + 'static,
+    T::Error: Send + Sync + 'static,
 {
     type Substream = SubstreamBox;
     type OutboundSubstream = usize; // TODO: use a newtype
@@ -48,18 +50,10 @@ where
         &self,
         cx: &mut Context<'_>,
     ) -> Poll<Result<StreamMuxerEvent<Self::Substream>, Self::Error>> {
-        let substream = match self.inner.poll_event(cx) {
-            Poll::Pending => return Poll::Pending,
-            Poll::Ready(Ok(StreamMuxerEvent::AddressChange(a))) => {
-                return Poll::Ready(Ok(StreamMuxerEvent::AddressChange(a)))
-            }
-            Poll::Ready(Ok(StreamMuxerEvent::InboundSubstream(s))) => s,
-            Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
-        };
+        let event = ready!(self.inner.poll_event(cx).map_err(into_io_error)?)
+            .map_inbound_stream(SubstreamBox::new);
 
-        Poll::Ready(Ok(StreamMuxerEvent::InboundSubstream(SubstreamBox::new(
-            substream,
-        ))))
+        Poll::Ready(Ok(event))
     }
 
     #[inline]
@@ -77,16 +71,12 @@ where
         substream: &mut Self::OutboundSubstream,
     ) -> Poll<Result<Self::Substream, Self::Error>> {
         let mut list = self.outbound.lock();
-        let substream = match self
+        let stream = ready!(self
             .inner
             .poll_outbound(cx, list.get_mut(substream).unwrap())
-        {
-            Poll::Pending => return Poll::Pending,
-            Poll::Ready(Ok(s)) => s,
-            Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
-        };
+            .map_err(into_io_error)?);
 
-        Poll::Ready(Ok(SubstreamBox::new(substream)))
+        Poll::Ready(Ok(SubstreamBox::new(stream)))
     }
 
     #[inline]
@@ -98,10 +88,17 @@ where
 
     #[inline]
     fn poll_close(&self, cx: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
-        self.inner.poll_close(cx).map_err(|e| e.into())
+        self.inner.poll_close(cx).map_err(into_io_error)
     }
 }
 
+fn into_io_error<E>(err: E) -> io::Error
+where
+    E: Error + Send + Sync + 'static,
+{
+    io::Error::new(io::ErrorKind::Other, err)
+}
+
 impl StreamMuxerBox {
     /// Turns a stream muxer into a `StreamMuxerBox`.
     pub fn new<T>(muxer: T) -> StreamMuxerBox
@@ -109,6 +106,7 @@ impl StreamMuxerBox {
         T: StreamMuxer + Send + Sync + 'static,
         T::OutboundSubstream: Send,
         T::Substream: Send + Unpin + 'static,
+        T::Error: Send + Sync + 'static,
     {
         let wrap = Wrap {
             inner: muxer,
diff --git a/core/src/transport/upgrade.rs b/core/src/transport/upgrade.rs
index 5f303396452..964045ad33f 100644
--- a/core/src/transport/upgrade.rs
+++ b/core/src/transport/upgrade.rs
@@ -302,6 +302,7 @@ impl<T> Multiplexed<T> {
         M: StreamMuxer + Send + Sync + 'static,
         M::Substream: Send + Unpin + 'static,
         M::OutboundSubstream: Send + 'static,
+        M::Error: Send + Sync + 'static,
     {
         boxed(self.map(|(i, m), _| (i, StreamMuxerBox::new(m))))
     }
diff --git a/swarm/src/connection.rs b/swarm/src/connection.rs
index e53701699e2..b09cb0480bd 100644
--- a/swarm/src/connection.rs
+++ b/swarm/src/connection.rs
@@ -137,40 +137,38 @@ where
     ) -> Poll<Result<Event<THandler::OutEvent>, ConnectionError<THandler::Error>>> {
         loop {
             // Poll the handler for new events.
-            match self.handler.poll(cx) {
+            match self.handler.poll(cx)? {
                 Poll::Pending => {}
-                Poll::Ready(Ok(handler_wrapper::Event::OutboundSubstreamRequest(user_data))) => {
+                Poll::Ready(handler_wrapper::Event::OutboundSubstreamRequest(user_data)) => {
                     self.muxing.open_substream(user_data);
                     continue;
                 }
-                Poll::Ready(Ok(handler_wrapper::Event::Custom(event))) => {
+                Poll::Ready(handler_wrapper::Event::Custom(event)) => {
                     return Poll::Ready(Ok(Event::Handler(event)));
                 }
-                Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
             }
 
             // Perform I/O on the connection through the muxer, informing the handler
             // of new substreams.
-            match self.muxing.poll(cx) {
+            match self.muxing.poll(cx)? {
                 Poll::Pending => {}
-                Poll::Ready(Ok(SubstreamEvent::InboundSubstream { substream })) => {
+                Poll::Ready(SubstreamEvent::InboundSubstream { substream }) => {
                     self.handler
                         .inject_substream(substream, SubstreamEndpoint::Listener);
                     continue;
                 }
-                Poll::Ready(Ok(SubstreamEvent::OutboundSubstream {
+                Poll::Ready(SubstreamEvent::OutboundSubstream {
                     user_data,
                     substream,
-                })) => {
+                }) => {
                     let endpoint = SubstreamEndpoint::Dialer(user_data);
                     self.handler.inject_substream(substream, endpoint);
                     continue;
                 }
-                Poll::Ready(Ok(SubstreamEvent::AddressChange(address))) => {
+                Poll::Ready(SubstreamEvent::AddressChange(address)) => {
                     self.handler.inject_address_change(&address);
                     return Poll::Ready(Ok(Event::AddressChange(address)));
                 }
-                Poll::Ready(Err(err)) => return Poll::Ready(Err(ConnectionError::IO(err))),
             }
 
             return Poll::Pending;
diff --git a/swarm/src/connection/error.rs b/swarm/src/connection/error.rs
index 4e8d85a8180..8a6d6bbbf00 100644
--- a/swarm/src/connection/error.rs
+++ b/swarm/src/connection/error.rs
@@ -75,6 +75,12 @@ impl<THandlerErr> From<handler_wrapper::Error<THandlerErr>> for ConnectionError<
     }
 }
 
+impl<THandlerErr> From<io::Error> for ConnectionError<THandlerErr> {
+    fn from(error: io::Error) -> Self {
+        ConnectionError::IO(error)
+    }
+}
+
 /// Errors that can occur in the context of a pending outgoing `Connection`.
 ///
 /// Note: Addresses for an outbound connection are dialed in parallel. Thus, compared to
diff --git a/swarm/src/connection/substream.rs b/swarm/src/connection/substream.rs
index 50714585366..47d5d315b20 100644
--- a/swarm/src/connection/substream.rs
+++ b/swarm/src/connection/substream.rs
@@ -23,7 +23,7 @@ use libp2p_core::multiaddr::Multiaddr;
 use libp2p_core::muxing::{StreamMuxer, StreamMuxerEvent};
 use smallvec::SmallVec;
 use std::sync::Arc;
-use std::{fmt, io::Error as IoError, pin::Pin, task::Context, task::Poll};
+use std::{fmt, pin::Pin, task::Context, task::Poll};
 
 /// Endpoint for a received substream.
 #[derive(Debug, Copy, Clone, PartialEq, Eq)]
@@ -134,7 +134,7 @@ where
     pub fn poll(
         &mut self,
         cx: &mut Context<'_>,
-    ) -> Poll<Result<SubstreamEvent<TMuxer, TUserData>, IoError>> {
+    ) -> Poll<Result<SubstreamEvent<TMuxer, TUserData>, TMuxer::Error>> {
         // Polling inbound substream.
         match self.inner.poll_event(cx) {
             Poll::Ready(Ok(StreamMuxerEvent::InboundSubstream(substream))) => {
@@ -143,7 +143,7 @@ where
             Poll::Ready(Ok(StreamMuxerEvent::AddressChange(addr))) => {
                 return Poll::Ready(Ok(SubstreamEvent::AddressChange(addr)))
             }
-            Poll::Ready(Err(err)) => return Poll::Ready(Err(err.into())),
+            Poll::Ready(Err(err)) => return Poll::Ready(Err(err)),
             Poll::Pending => {}
         }
 
@@ -164,7 +164,7 @@ where
                 }
                 Poll::Ready(Err(err)) => {
                     self.inner.destroy_outbound(outbound);
-                    return Poll::Ready(Err(err.into()));
+                    return Poll::Ready(Err(err));
                 }
             }
         }
@@ -203,13 +203,13 @@ impl<TMuxer> Future for Close<TMuxer>
 where
     TMuxer: StreamMuxer,
 {
-    type Output = Result<(), IoError>;
+    type Output = Result<(), TMuxer::Error>;
 
     fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
         match self.muxer.poll_close(cx) {
             Poll::Pending => Poll::Pending,
             Poll::Ready(Ok(())) => Poll::Ready(Ok(())),
-            Poll::Ready(Err(err)) => Poll::Ready(Err(err.into())),
+            Poll::Ready(Err(err)) => Poll::Ready(Err(err)),
         }
     }
 }