diff --git a/src/client/conn/http1.rs b/src/client/conn/http1.rs
index b78757b9ca..bd3d44a7f8 100644
--- a/src/client/conn/http1.rs
+++ b/src/client/conn/http1.rs
@@ -11,6 +11,7 @@ use bytes::Bytes;
 use futures_core::ready;
 use http::{Request, Response};
 use httparse::ParserConfig;
+use tokio::sync::oneshot::Receiver;
 
 use super::super::dispatch::{self, TrySendError};
 use crate::body::{Body, Incoming as IncomingBody};
@@ -210,26 +211,12 @@ where
     /// hyper closes the underlying connection when a request future is
     /// dropped before completion. Any subsequent calls on the same
     /// [`SendRequest`] will return a `canceled` error.
-    pub fn send_request(
-        &mut self,
-        req: Request<B>,
-    ) -> impl Future<Output = crate::Result<Response<IncomingBody>>> {
-        let sent = self.dispatch.send(req);
-
-        async move {
-            match sent {
-                Ok(rx) => match rx.await {
-                    Ok(Ok(resp)) => Ok(resp),
-                    Ok(Err(err)) => Err(err),
-                    // this is definite bug if it happens, but it shouldn't happen!
-                    Err(_canceled) => panic!("dispatch dropped without returning error"),
-                },
-                Err(_req) => {
-                    debug!("connection was not ready");
-                    Err(crate::Error::new_canceled().with("connection was not ready"))
-                }
-            }
-        }
+    pub fn send_request(&mut self, req: Request<B>) -> SendFut {
+        let state = match self.dispatch.send(req) {
+            Ok(rx) => SendFutState::Fut { rx },
+            Err(_) => SendFutState::Err,
+        };
+        SendFut { state }
     }
 
     /// Sends a `Request` on the associated connection.
@@ -240,29 +227,14 @@ where
     ///
     /// If there was an error before trying to serialize the request to the
     /// connection, the message will be returned as part of this error.
-    pub fn try_send_request(
-        &mut self,
-        req: Request<B>,
-    ) -> impl Future<Output = Result<Response<IncomingBody>, TrySendError<Request<B>>>> {
-        let sent = self.dispatch.try_send(req);
-        async move {
-            match sent {
-                Ok(rx) => match rx.await {
-                    Ok(Ok(res)) => Ok(res),
-                    Ok(Err(err)) => Err(err),
-                    // this is definite bug if it happens, but it shouldn't happen!
-                    Err(_) => panic!("dispatch dropped without returning error"),
-                },
-                Err(req) => {
-                    debug!("connection was not ready");
-                    let error = crate::Error::new_canceled().with("connection was not ready");
-                    Err(TrySendError {
-                        error,
-                        message: Some(req),
-                    })
-                }
-            }
-        }
+    pub fn try_send_request(&mut self, req: Request<B>) -> TrySendFut<B> {
+        let state = match self.dispatch.try_send(req) {
+            Ok(rx) => TrySendFutState::Fut { rx },
+            Err(req) => TrySendFutState::Err {
+                req: Box::new(Some(req)),
+            },
+        };
+        TrySendFut { state }
     }
 }
 
@@ -272,6 +244,89 @@ impl<B> fmt::Debug for SendRequest<B> {
     }
 }
 
+enum SendFutState {
+    Fut {
+        rx: Receiver<crate::Result<Response<IncomingBody>>>,
+    },
+    Err,
+}
+
+/// Future returned by [`SendRequest::send_request`], see the method definition
+/// for more details.
+pub struct SendFut {
+    state: SendFutState,
+}
+
+impl fmt::Debug for SendFut {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("SendFut").finish()
+    }
+}
+
+impl Future for SendFut {
+    type Output = crate::Result<Response<IncomingBody>>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let res = match &mut self.state {
+            SendFutState::Fut { rx } => match ready!(Pin::new(rx).poll(cx)) {
+                Ok(Ok(resp)) => Ok(resp),
+                Ok(Err(err)) => Err(err),
+                // this is definite bug if it happens, but it shouldn't happen!
+                Err(_) => panic!("dispatch dropped without returning error"),
+            },
+            SendFutState::Err => {
+                debug!("connection was not ready");
+                Err(crate::Error::new_canceled().with("connection was not ready"))
+            }
+        };
+        Poll::Ready(res)
+    }
+}
+
+enum TrySendFutState<B> {
+    Fut {
+        rx: Receiver<Result<Response<IncomingBody>, TrySendError<Request<B>>>>,
+    },
+    Err {
+        req: Box<Option<Request<B>>>,
+    },
+}
+
+/// Future returned by [`SendRequest::try_send_request`], see the method
+/// definition for more details.
+pub struct TrySendFut<B> {
+    state: TrySendFutState<B>,
+}
+
+impl<B> fmt::Debug for TrySendFut<B> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("TrySendFut").finish()
+    }
+}
+
+impl<B> Future for TrySendFut<B> {
+    type Output = Result<Response<IncomingBody>, TrySendError<Request<B>>>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let res = match &mut self.state {
+            TrySendFutState::Fut { rx } => match ready!(Pin::new(rx).poll(cx)) {
+                Ok(Ok(resp)) => Ok(resp),
+                Ok(Err(err)) => Err(err),
+                // this is definite bug if it happens, but it shouldn't happen!
+                Err(_) => panic!("dispatch dropped without returning error"),
+            },
+            TrySendFutState::Err { req } => {
+                debug!("connection was not ready");
+                Err(TrySendError {
+                    error: crate::Error::new_canceled().with("connection was not ready"),
+                    message: Some(req.take().expect("future already resolved")),
+                })
+            }
+        };
+        Poll::Ready(res)
+    }
+}
+
 // ===== impl Connection
 
 impl<T, B> Connection<T, B>
diff --git a/src/client/conn/http2.rs b/src/client/conn/http2.rs
index 5ffad524be..bf13b401f6 100644
--- a/src/client/conn/http2.rs
+++ b/src/client/conn/http2.rs
@@ -12,6 +12,7 @@ use std::time::Duration;
 use crate::rt::{Read, Write};
 use futures_core::ready;
 use http::{Request, Response};
+use tokio::sync::oneshot::Receiver;
 
 use super::super::dispatch::{self, TrySendError};
 use crate::body::{Body, Incoming as IncomingBody};
@@ -147,27 +148,12 @@ where
     /// other in-flight and future requests. The peer is notified
     /// immediately rather than continuing to send a response body that
     /// would be discarded.
-    pub fn send_request(
-        &mut self,
-        req: Request<B>,
-    ) -> impl Future<Output = crate::Result<Response<IncomingBody>>> {
-        let sent = self.dispatch.send(req);
-
-        async move {
-            match sent {
-                Ok(rx) => match rx.await {
-                    Ok(Ok(resp)) => Ok(resp),
-                    Ok(Err(err)) => Err(err),
-                    // this is definite bug if it happens, but it shouldn't happen!
-                    Err(_canceled) => panic!("dispatch dropped without returning error"),
-                },
-                Err(_req) => {
-                    debug!("connection was not ready");
-
-                    Err(crate::Error::new_canceled().with("connection was not ready"))
-                }
-            }
-        }
+    pub fn send_request(&mut self, req: Request<B>) -> SendFut {
+        let state = match self.dispatch.send(req) {
+            Ok(rx) => SendFutState::Fut { rx },
+            Err(_) => SendFutState::Err,
+        };
+        SendFut { state }
     }
 
     /// Sends a `Request` on the associated connection.
@@ -178,29 +164,14 @@ where
     ///
     /// If there was an error before trying to serialize the request to the
     /// connection, the message will be returned as part of this error.
-    pub fn try_send_request(
-        &mut self,
-        req: Request<B>,
-    ) -> impl Future<Output = Result<Response<IncomingBody>, TrySendError<Request<B>>>> {
-        let sent = self.dispatch.try_send(req);
-        async move {
-            match sent {
-                Ok(rx) => match rx.await {
-                    Ok(Ok(res)) => Ok(res),
-                    Ok(Err(err)) => Err(err),
-                    // this is definite bug if it happens, but it shouldn't happen!
-                    Err(_) => panic!("dispatch dropped without returning error"),
-                },
-                Err(req) => {
-                    debug!("connection was not ready");
-                    let error = crate::Error::new_canceled().with("connection was not ready");
-                    Err(TrySendError {
-                        error,
-                        message: Some(req),
-                    })
-                }
-            }
-        }
+    pub fn try_send_request(&mut self, req: Request<B>) -> TrySendFut<B> {
+        let state = match self.dispatch.try_send(req) {
+            Ok(rx) => TrySendFutState::Fut { rx },
+            Err(req) => TrySendFutState::Err {
+                req: Box::new(Some(req)),
+            },
+        };
+        TrySendFut { state }
     }
 }
 
@@ -210,6 +181,89 @@ impl<B> fmt::Debug for SendRequest<B> {
     }
 }
 
+enum SendFutState {
+    Fut {
+        rx: Receiver<crate::Result<Response<IncomingBody>>>,
+    },
+    Err,
+}
+
+/// Future returned by [`SendRequest::send_request`], see the method definition
+/// for more details.
+pub struct SendFut {
+    state: SendFutState,
+}
+
+impl fmt::Debug for SendFut {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("SendFut").finish()
+    }
+}
+
+impl Future for SendFut {
+    type Output = crate::Result<Response<IncomingBody>>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let res = match &mut self.state {
+            SendFutState::Fut { rx } => match ready!(Pin::new(rx).poll(cx)) {
+                Ok(Ok(resp)) => Ok(resp),
+                Ok(Err(err)) => Err(err),
+                // this is definite bug if it happens, but it shouldn't happen!
+                Err(_) => panic!("dispatch dropped without returning error"),
+            },
+            SendFutState::Err => {
+                debug!("connection was not ready");
+                Err(crate::Error::new_canceled().with("connection was not ready"))
+            }
+        };
+        Poll::Ready(res)
+    }
+}
+
+enum TrySendFutState<B> {
+    Fut {
+        rx: Receiver<Result<Response<IncomingBody>, TrySendError<Request<B>>>>,
+    },
+    Err {
+        req: Box<Option<Request<B>>>,
+    },
+}
+
+/// Future returned by [`SendRequest::try_send_request`], see the method
+/// definition for more details.
+pub struct TrySendFut<B> {
+    state: TrySendFutState<B>,
+}
+
+impl<B> fmt::Debug for TrySendFut<B> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("TrySendFut").finish()
+    }
+}
+
+impl<B> Future for TrySendFut<B> {
+    type Output = Result<Response<IncomingBody>, TrySendError<Request<B>>>;
+
+    fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let res = match &mut self.state {
+            TrySendFutState::Fut { rx } => match ready!(Pin::new(rx).poll(cx)) {
+                Ok(Ok(resp)) => Ok(resp),
+                Ok(Err(err)) => Err(err),
+                // this is definite bug if it happens, but it shouldn't happen!
+                Err(_) => panic!("dispatch dropped without returning error"),
+            },
+            TrySendFutState::Err { req } => {
+                debug!("connection was not ready");
+                Err(TrySendError {
+                    error: crate::Error::new_canceled().with("connection was not ready"),
+                    message: Some(req.take().expect("future already resolved")),
+                })
+            }
+        };
+        Poll::Ready(res)
+    }
+}
+
 // ===== impl Connection
 
 impl<T, B, E> Connection<T, B, E>