diff --git a/src/common/drain.rs b/src/common/drain.rs
index e98f5b34..4f04fd61 100644
--- a/src/common/drain.rs
+++ b/src/common/drain.rs
@@ -1,37 +1,23 @@
 use std::mem;
 
 use pin_project::pin_project;
-use tokio::stream::Stream;
-use tokio::sync::{mpsc, watch};
+use tokio::sync::watch;
 
-use super::{task, Future, Never, Pin, Poll};
+use super::{task, Future, Pin, Poll};
 
 pub fn channel() -> (Signal, Watch) {
     let (tx, rx) = watch::channel(());
-    let (drained_tx, drained_rx) = mpsc::channel(1);
-    (
-        Signal {
-            drained_rx,
-            _tx: tx,
-        },
-        Watch { drained_tx, rx },
-    )
+    (Signal { tx }, Watch { rx })
 }
 
 pub struct Signal {
-    drained_rx: mpsc::Receiver<Never>,
-    _tx: watch::Sender<()>,
+    tx: watch::Sender<()>,
 }
 
-#[pin_project::pin_project]
-pub struct Draining {
-    #[pin]
-    drained_rx: mpsc::Receiver<Never>,
-}
+pub struct Draining(Pin<Box<dyn Future<Output = ()> + Send + Sync>>);
 
 #[derive(Clone)]
 pub struct Watch {
-    drained_tx: mpsc::Sender<Never>,
     rx: watch::Receiver<()>,
 }
 
@@ -42,7 +28,7 @@ pub struct Watching<F, FN> {
     future: F,
     state: State<FN>,
     watch: Pin<Box<dyn Future<Output = ()> + Send + Sync>>,
-    _drained_tx: mpsc::Sender<Never>,
+    _rx: watch::Receiver<()>,
 }
 
 enum State<F> {
@@ -52,21 +38,16 @@ enum State<F> {
 
 impl Signal {
     pub fn drain(self) -> Draining {
-        // Simply dropping `self.tx` will signal the watchers
-        Draining {
-            drained_rx: self.drained_rx,
-        }
+        let _ = self.tx.send(());
+        Draining(Box::pin(async move { self.tx.closed().await }))
     }
 }
 
 impl Future for Draining {
     type Output = ();
 
-    fn poll(self: Pin<&mut Self>, cx: &mut task::Context<'_>) -> Poll<Self::Output> {
-        match ready!(self.project().drained_rx.poll_next(cx)) {
-            Some(never) => match never {},
-            None => Poll::Ready(()),
-        }
+    fn poll(mut self: Pin<&mut Self>, cx: &mut task::Context<'_>) -> Poll<Self::Output> {
+        Pin::new(&mut self.as_mut().0).poll(cx)
     }
 }
 
@@ -76,14 +57,17 @@ impl Watch {
         F: Future,
         FN: FnOnce(Pin<&mut F>),
     {
-        let Self { drained_tx, mut rx } = self;
+        let Self { mut rx } = self;
+        let _rx = rx.clone();
         Watching {
             future,
             state: State::Watch(on_drain),
             watch: Box::pin(async move {
                 let _ = rx.changed().await;
             }),
-            _drained_tx: drained_tx,
+            // Keep the receiver alive until the future completes, so that
+            // dropping it can signal that draining has completed.
+            _rx,
         }
     }
 }