diff --git a/tokio-util/src/future.rs b/tokio-util/src/future.rs
index ba4779908..408de66b9 100644
--- a/tokio-util/src/future.rs
+++ b/tokio-util/src/future.rs
@@ -59,14 +59,13 @@ pub trait FutureExt: Future {
     }
 
     /// Similar to [`CancellationToken::run_until_cancelled`],
-    /// but with the advantage that it is easier to write fluent call chains,
-    /// and biased towards waiting for [`CancellationToken`] to complete.
+    /// but with the advantage that it is easier to write fluent call chains.
     ///
     /// # 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, this is biased towards the `self` future completion.
     ///
     /// # Examples
     ///
@@ -97,14 +96,13 @@ pub trait FutureExt: Future {
     }
 
     /// Similar to [`CancellationToken::run_until_cancelled_owned`],
-    /// but with the advantage that it is easier to write fluent call chains,
-    /// and biased towards waiting for [`CancellationToken`] to complete.
+    /// but with the advantage that it is easier to write fluent call chains.
     ///
     /// # 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, this is biased towards the `self` future completion.
     ///
     /// # Examples
     ///