diff --git a/tokio-util/src/sync/cancellation_token.rs b/tokio-util/src/sync/cancellation_token.rs
index 40a8ae867b6..d785ed424de 100644
--- a/tokio-util/src/sync/cancellation_token.rs
+++ b/tokio-util/src/sync/cancellation_token.rs
@@ -268,6 +268,12 @@ impl CancellationToken {
     /// unless the [`CancellationToken`] is cancelled. In that case the function returns
     /// `None` and the future gets dropped.
     ///
+    /// # Fairness
+    ///
+    /// Calling this on an already-cancelled token directly returns `None`.
+    /// For all subsequent polls, in case of concurrent completion and
+    /// cancellation, this is biased towards the future completion.
+    ///
     /// # Cancellation safety
     ///
     /// This method is only cancel safe if `fut` is cancel safe.
@@ -293,21 +299,25 @@ impl CancellationToken {
 
             fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
                 let this = self.project();
-                if this.cancellation.poll(cx).is_ready() {
-                    Poll::Ready(None)
-                } else if let Poll::Ready(res) = this.future.poll(cx) {
+                if let Poll::Ready(res) = this.future.poll(cx) {
                     Poll::Ready(Some(res))
+                } else if this.cancellation.poll(cx).is_ready() {
+                    Poll::Ready(None)
                 } else {
                     Poll::Pending
                 }
             }
         }
 
-        RunUntilCancelledFuture {
-            cancellation: self.cancelled(),
-            future: fut,
+        if self.is_cancelled() {
+            None
+        } else {
+            RunUntilCancelledFuture {
+                cancellation: self.cancelled(),
+                future: fut,
+            }
+            .await
         }
-        .await
     }
 
     /// Runs a future to completion and returns its result wrapped inside of an `Option`
@@ -316,6 +326,12 @@ impl CancellationToken {
     ///
     /// The function takes self by value and returns a future that owns the token.
     ///
+    /// # Fairness
+    ///
+    /// Calling this on an already-cancelled token directly returns `None`.
+    /// For all subsequent polls, in case of concurrent completion and
+    /// cancellation, this is biased towards the future completion.
+    ///
     /// # Cancellation safety
     ///
     /// This method is only cancel safe if `fut` is cancel safe.