diff --git a/tests/h2-support/src/future_ext.rs b/tests/h2-support/src/future_ext.rs
index 9f659b34..cca18c66 100644
--- a/tests/h2-support/src/future_ext.rs
+++ b/tests/h2-support/src/future_ext.rs
@@ -1,7 +1,9 @@
-use futures::FutureExt;
+use futures::{FutureExt, TryFuture};
 use std::future::Future;
 use std::pin::Pin;
-use std::task::{Context, Poll};
+use std::sync::atomic::AtomicBool;
+use std::sync::Arc;
+use std::task::{Context, Poll, Wake, Waker};
 
 /// Future extension helpers that are useful for tests
 pub trait TestFuture: Future {
@@ -15,9 +17,140 @@ pub trait TestFuture: Future {
     {
         Drive {
             driver: self,
-            future: Box::pin(other),
+            future: other.wakened(),
         }
     }
+
+    fn wakened(self) -> Wakened<Self>
+    where
+        Self: Sized,
+    {
+        Wakened {
+            future: Box::pin(self),
+            woken: Arc::new(AtomicBool::new(true)),
+        }
+    }
+}
+
+/// Wraps futures::future::join to ensure that the futures are only polled if they are woken.
+pub fn join<Fut1, Fut2>(
+    future1: Fut1,
+    future2: Fut2,
+) -> futures::future::Join<Wakened<Fut1>, Wakened<Fut2>>
+where
+    Fut1: Future,
+    Fut2: Future,
+{
+    futures::future::join(future1.wakened(), future2.wakened())
+}
+
+/// Wraps futures::future::join3 to ensure that the futures are only polled if they are woken.
+pub fn join3<Fut1, Fut2, Fut3>(
+    future1: Fut1,
+    future2: Fut2,
+    future3: Fut3,
+) -> futures::future::Join3<Wakened<Fut1>, Wakened<Fut2>, Wakened<Fut3>>
+where
+    Fut1: Future,
+    Fut2: Future,
+    Fut3: Future,
+{
+    futures::future::join3(future1.wakened(), future2.wakened(), future3.wakened())
+}
+
+/// Wraps futures::future::join4 to ensure that the futures are only polled if they are woken.
+pub fn join4<Fut1, Fut2, Fut3, Fut4>(
+    future1: Fut1,
+    future2: Fut2,
+    future3: Fut3,
+    future4: Fut4,
+) -> futures::future::Join4<Wakened<Fut1>, Wakened<Fut2>, Wakened<Fut3>, Wakened<Fut4>>
+where
+    Fut1: Future,
+    Fut2: Future,
+    Fut3: Future,
+    Fut4: Future,
+{
+    futures::future::join4(
+        future1.wakened(),
+        future2.wakened(),
+        future3.wakened(),
+        future4.wakened(),
+    )
+}
+
+/// Wraps futures::future::try_join to ensure that the futures are only polled if they are woken.
+pub fn try_join<Fut1, Fut2>(
+    future1: Fut1,
+    future2: Fut2,
+) -> futures::future::TryJoin<Wakened<Fut1>, Wakened<Fut2>>
+where
+    Fut1: futures::future::TryFuture + Future,
+    Fut2: Future,
+    Wakened<Fut1>: futures::future::TryFuture,
+    Wakened<Fut2>: futures::future::TryFuture<Error = <Wakened<Fut1> as TryFuture>::Error>,
+{
+    futures::future::try_join(future1.wakened(), future2.wakened())
+}
+
+/// Wraps futures::future::select to ensure that the futures are only polled if they are woken.
+pub fn select<A, B>(future1: A, future2: B) -> futures::future::Select<Wakened<A>, Wakened<B>>
+where
+    A: Future + Unpin,
+    B: Future + Unpin,
+{
+    futures::future::select(future1.wakened(), future2.wakened())
+}
+
+/// Wraps futures::future::join_all to ensure that the futures are only polled if they are woken.
+pub fn join_all<I>(iter: I) -> futures::future::JoinAll<Wakened<I::Item>>
+where
+    I: IntoIterator,
+    I::Item: Future,
+{
+    futures::future::join_all(iter.into_iter().map(|f| f.wakened()))
+}
+
+/// A future that only polls the inner future if it has been woken (after the initial poll).
+pub struct Wakened<T> {
+    future: Pin<Box<T>>,
+    woken: Arc<AtomicBool>,
+}
+
+/// A future that only polls the inner future if it has been woken (after the initial poll).
+impl<T> Future for Wakened<T>
+where
+    T: Future,
+{
+    type Output = T::Output;
+
+    fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let this = self.get_mut();
+        if !this.woken.load(std::sync::atomic::Ordering::SeqCst) {
+            return Poll::Pending;
+        }
+        this.woken.store(false, std::sync::atomic::Ordering::SeqCst);
+        let my_waker = IfWokenWaker {
+            inner: cx.waker().clone(),
+            wakened: this.woken.clone(),
+        };
+        let my_waker = Arc::new(my_waker).into();
+        let mut cx = Context::from_waker(&my_waker);
+        this.future.as_mut().poll(&mut cx)
+    }
+}
+
+impl Wake for IfWokenWaker {
+    fn wake(self: Arc<Self>) {
+        self.wakened
+            .store(true, std::sync::atomic::Ordering::SeqCst);
+        self.inner.wake_by_ref();
+    }
+}
+
+struct IfWokenWaker {
+    inner: Waker,
+    wakened: Arc<AtomicBool>,
 }
 
 impl<T: Future> TestFuture for T {}
@@ -29,7 +162,7 @@ impl<T: Future> TestFuture for T {}
 /// This is useful for H2 futures that also require the connection to be polled.
 pub struct Drive<'a, T, U> {
     driver: &'a mut T,
-    future: Pin<Box<U>>,
+    future: Wakened<U>,
 }
 
 impl<'a, T, U> Future for Drive<'a, T, U>
diff --git a/tests/h2-support/src/prelude.rs b/tests/h2-support/src/prelude.rs
index c40a518d..3c6e15d7 100644
--- a/tests/h2-support/src/prelude.rs
+++ b/tests/h2-support/src/prelude.rs
@@ -35,7 +35,7 @@ pub use {bytes, futures, http, tokio::io as tokio_io, tracing, tracing_subscribe
 pub use futures::{Future, Sink, Stream};
 
 // And our Future extensions
-pub use super::future_ext::TestFuture;
+pub use super::future_ext::{TestFuture, join, join_all, select, join3, join4, try_join};
 
 // Our client_ext helpers
 pub use super::client_ext::SendRequestExt;
diff --git a/tests/h2-tests/tests/client_request.rs b/tests/h2-tests/tests/client_request.rs
index 50be06e6..8e0e599a 100644
--- a/tests/h2-tests/tests/client_request.rs
+++ b/tests/h2-tests/tests/client_request.rs
@@ -1,4 +1,4 @@
-use futures::future::{join, join_all, ready, select, Either};
+use futures::future::{ready, Either};
 use futures::stream::FuturesUnordered;
 use futures::StreamExt;
 use h2_support::prelude::*;
@@ -849,7 +849,7 @@ async fn recv_too_big_headers() {
     };
 
     let client = async move {
-        let (mut client, conn) = client::Builder::new()
+        let (mut client, mut conn) = client::Builder::new()
             .max_header_list_size(10)
             .handshake::<_, Bytes>(io)
             .await
@@ -863,10 +863,10 @@ async fn recv_too_big_headers() {
         let req1 = client.send_request(request, true);
         // Spawn tasks to ensure that the error wakes up tasks that are blocked
         // waiting for a response.
-        let req1 = tokio::spawn(async move {
+        let req1 = async move {
             let err = req1.expect("send_request").0.await.expect_err("response1");
             assert_eq!(err.reason(), Some(Reason::REFUSED_STREAM));
-        });
+        };
 
         let request = Request::builder()
             .uri("https://http2.akamai.com/")
@@ -874,19 +874,13 @@ async fn recv_too_big_headers() {
             .unwrap();
 
         let req2 = client.send_request(request, true);
-        let req2 = tokio::spawn(async move {
+        let req2 = async move {
             let err = req2.expect("send_request").0.await.expect_err("response2");
             assert_eq!(err.reason(), Some(Reason::REFUSED_STREAM));
-        });
+        };
 
-        let conn = tokio::spawn(async move {
-            conn.await.expect("client");
-        });
-        for err in join_all([req1, req2, conn]).await {
-            if let Some(err) = err.err().and_then(|err| err.try_into_panic().ok()) {
-                std::panic::resume_unwind(err);
-            }
-        }
+
+        conn.drive(join(req1, req2)).await;
     };
 
     join(srv, client).await;
diff --git a/tests/h2-tests/tests/codec_read.rs b/tests/h2-tests/tests/codec_read.rs
index d955e186..489d16da 100644
--- a/tests/h2-tests/tests/codec_read.rs
+++ b/tests/h2-tests/tests/codec_read.rs
@@ -1,4 +1,3 @@
-use futures::future::join;
 use h2_support::prelude::*;
 
 #[tokio::test]
diff --git a/tests/h2-tests/tests/codec_write.rs b/tests/h2-tests/tests/codec_write.rs
index 0b85a223..04627cdc 100644
--- a/tests/h2-tests/tests/codec_write.rs
+++ b/tests/h2-tests/tests/codec_write.rs
@@ -1,4 +1,3 @@
-use futures::future::join;
 use h2_support::prelude::*;
 
 #[tokio::test]
diff --git a/tests/h2-tests/tests/flow_control.rs b/tests/h2-tests/tests/flow_control.rs
index dbb93328..e3caaff5 100644
--- a/tests/h2-tests/tests/flow_control.rs
+++ b/tests/h2-tests/tests/flow_control.rs
@@ -1,4 +1,3 @@
-use futures::future::{join, join4};
 use futures::{StreamExt, TryStreamExt};
 use h2_support::prelude::*;
 use h2_support::util::yield_once;
diff --git a/tests/h2-tests/tests/ping_pong.rs b/tests/h2-tests/tests/ping_pong.rs
index 0f93578c..2132c7ac 100644
--- a/tests/h2-tests/tests/ping_pong.rs
+++ b/tests/h2-tests/tests/ping_pong.rs
@@ -1,5 +1,4 @@
 use futures::channel::oneshot;
-use futures::future::join;
 use futures::StreamExt;
 use h2_support::assert_ping;
 use h2_support::prelude::*;
diff --git a/tests/h2-tests/tests/prioritization.rs b/tests/h2-tests/tests/prioritization.rs
index 11d2c2cc..dd4ed9fe 100644
--- a/tests/h2-tests/tests/prioritization.rs
+++ b/tests/h2-tests/tests/prioritization.rs
@@ -1,4 +1,3 @@
-use futures::future::{join, select};
 use futures::{pin_mut, FutureExt, StreamExt};
 
 use h2_support::prelude::*;
diff --git a/tests/h2-tests/tests/push_promise.rs b/tests/h2-tests/tests/push_promise.rs
index c2138edc..fbc37558 100644
--- a/tests/h2-tests/tests/push_promise.rs
+++ b/tests/h2-tests/tests/push_promise.rs
@@ -1,6 +1,4 @@
-use std::iter::FromIterator;
-
-use futures::{future::join, FutureExt as _, StreamExt, TryStreamExt};
+use futures::{StreamExt, TryStreamExt};
 use h2_support::prelude::*;
 
 #[tokio::test]
@@ -52,15 +50,9 @@ async fn recv_push_works() {
             let ps: Vec<_> = p.collect().await;
             assert_eq!(1, ps.len())
         };
-        // Use a FuturesUnordered to poll both tasks but only poll them
-        // if they have been notified.
-        let tasks = futures::stream::FuturesUnordered::from_iter([
-            check_resp_status.boxed(),
-            check_pushed_response.boxed(),
-        ])
-        .collect::<()>();
-
-        h2.drive(tasks).await;
+
+        h2.drive(join(check_resp_status, check_pushed_response))
+            .await;
     };
 
     join(mock, h2).await;
diff --git a/tests/h2-tests/tests/server.rs b/tests/h2-tests/tests/server.rs
index 7155b586..c266bc2d 100644
--- a/tests/h2-tests/tests/server.rs
+++ b/tests/h2-tests/tests/server.rs
@@ -1,6 +1,5 @@
 #![deny(warnings)]
 
-use futures::future::join;
 use futures::StreamExt;
 use h2_support::prelude::*;
 use tokio::io::AsyncWriteExt;
diff --git a/tests/h2-tests/tests/stream_states.rs b/tests/h2-tests/tests/stream_states.rs
index 05a96a0f..9a377d79 100644
--- a/tests/h2-tests/tests/stream_states.rs
+++ b/tests/h2-tests/tests/stream_states.rs
@@ -1,6 +1,6 @@
 #![deny(warnings)]
 
-use futures::future::{join, join3, lazy, try_join};
+use futures::future::lazy;
 use futures::{FutureExt, StreamExt, TryStreamExt};
 use h2_support::prelude::*;
 use h2_support::util::yield_once;