diff --git a/src/client/conn/http1.rs b/src/client/conn/http1.rs
index 2e91209861..4ea780610d 100644
--- a/src/client/conn/http1.rs
+++ b/src/client/conn/http1.rs
@@ -51,7 +51,7 @@ pub struct Parts<T> {
 #[must_use = "futures do nothing unless polled"]
 pub struct Connection<T, B>
 where
-    T: Read + Write + 'static,
+    T: Read + Write,
     B: Body + 'static,
 {
     inner: Dispatcher<T, B>,
@@ -59,7 +59,7 @@ where
 
 impl<T, B> Connection<T, B>
 where
-    T: Read + Write + Unpin + 'static,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     B::Error: Into<Box<dyn StdError + Send + Sync>>,
 {
@@ -124,7 +124,7 @@ pub struct Builder {
 /// See [`client::conn`](crate::client::conn) for more.
 pub async fn handshake<T, B>(io: T) -> crate::Result<(SendRequest<B>, Connection<T, B>)>
 where
-    T: Read + Write + Unpin + 'static,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     B::Data: Send,
     B::Error: Into<Box<dyn StdError + Send + Sync>>,
@@ -247,7 +247,7 @@ impl<B> fmt::Debug for SendRequest<B> {
 
 impl<T, B> Connection<T, B>
 where
-    T: Read + Write + Unpin + Send + 'static,
+    T: Read + Write + Unpin + Send,
     B: Body + 'static,
     B::Error: Into<Box<dyn StdError + Send + Sync>>,
 {
@@ -261,7 +261,7 @@ where
 
 impl<T, B> fmt::Debug for Connection<T, B>
 where
-    T: Read + Write + fmt::Debug + 'static,
+    T: Read + Write + fmt::Debug,
     B: Body + 'static,
 {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
@@ -271,7 +271,7 @@ where
 
 impl<T, B> Future for Connection<T, B>
 where
-    T: Read + Write + Unpin + 'static,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     B::Data: Send,
     B::Error: Into<Box<dyn StdError + Send + Sync>>,
@@ -509,7 +509,7 @@ impl Builder {
         io: T,
     ) -> impl Future<Output = crate::Result<(SendRequest<B>, Connection<T, B>)>>
     where
-        T: Read + Write + Unpin + 'static,
+        T: Read + Write + Unpin,
         B: Body + 'static,
         B::Data: Send,
         B::Error: Into<Box<dyn StdError + Send + Sync>>,
diff --git a/src/client/conn/http2.rs b/src/client/conn/http2.rs
index df78691901..c7938e303b 100644
--- a/src/client/conn/http2.rs
+++ b/src/client/conn/http2.rs
@@ -40,7 +40,7 @@ impl<B> Clone for SendRequest<B> {
 #[must_use = "futures do nothing unless polled"]
 pub struct Connection<T, B, E>
 where
-    T: Read + Write + 'static + Unpin,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     E: Http2ClientConnExec<B, T> + Unpin,
     B::Error: Into<Box<dyn Error + Send + Sync>>,
@@ -70,7 +70,7 @@ pub async fn handshake<E, T, B>(
     io: T,
 ) -> crate::Result<(SendRequest<B>, Connection<T, B, E>)>
 where
-    T: Read + Write + Unpin + 'static,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     B::Data: Send,
     B::Error: Into<Box<dyn Error + Send + Sync>>,
@@ -432,7 +432,7 @@ where
         io: T,
     ) -> impl Future<Output = crate::Result<(SendRequest<B>, Connection<T, B, Ex>)>>
     where
-        T: Read + Write + Unpin + 'static,
+        T: Read + Write + Unpin,
         B: Body + 'static,
         B::Data: Send,
         B::Error: Into<Box<dyn Error + Send + Sync>>,
diff --git a/src/proto/h1/dispatch.rs b/src/proto/h1/dispatch.rs
index be0a88c1f9..dabcff6be3 100644
--- a/src/proto/h1/dispatch.rs
+++ b/src/proto/h1/dispatch.rs
@@ -107,10 +107,10 @@ where
     ///
     /// This is useful for old-style HTTP upgrades, but ignores
     /// newer-style upgrade API.
-    pub(crate) fn poll_without_shutdown(&mut self, cx: &mut Context<'_>) -> Poll<crate::Result<()>>
-    where
-        Self: Unpin,
-    {
+    pub(crate) fn poll_without_shutdown(
+        &mut self,
+        cx: &mut Context<'_>,
+    ) -> Poll<crate::Result<()>> {
         Pin::new(self).poll_catch(cx, false).map_ok(|ds| {
             if let Dispatched::Upgrade(pending) = ds {
                 pending.manual();
diff --git a/src/proto/h2/client.rs b/src/proto/h2/client.rs
index 7cb6c6ed5b..6675142118 100644
--- a/src/proto/h2/client.rs
+++ b/src/proto/h2/client.rs
@@ -137,7 +137,7 @@ pub(crate) async fn handshake<T, B, E>(
     timer: Time,
 ) -> crate::Result<ClientTask<B, E, T>>
 where
-    T: Read + Write + Unpin + 'static,
+    T: Read + Write + Unpin,
     B: Body + 'static,
     B::Data: Send + 'static,
     E: Http2ClientConnExec<B, T> + Unpin,
diff --git a/src/server/conn/http1.rs b/src/server/conn/http1.rs
index cf22316296..a1e3325785 100644
--- a/src/server/conn/http1.rs
+++ b/src/server/conn/http1.rs
@@ -166,7 +166,6 @@ where
     where
         S: Unpin,
         S::Future: Unpin,
-        B: Unpin,
     {
         self.conn.poll_without_shutdown(cx)
     }
@@ -177,12 +176,7 @@ where
     /// # Error
     ///
     /// This errors if the underlying connection protocol is not HTTP/1.
-    pub fn without_shutdown(self) -> impl Future<Output = crate::Result<Parts<I, S>>>
-    where
-        S: Unpin,
-        S::Future: Unpin,
-        B: Unpin,
-    {
+    pub fn without_shutdown(self) -> impl Future<Output = crate::Result<Parts<I, S>>> {
         let mut zelf = Some(self);
         futures_util::future::poll_fn(move |cx| {
             ready!(zelf.as_mut().unwrap().conn.poll_without_shutdown(cx))?;