diff --git a/core/shared/src/main/scala/fs2/Stream.scala b/core/shared/src/main/scala/fs2/Stream.scala
index a3642794a8..f0711506f2 100644
--- a/core/shared/src/main/scala/fs2/Stream.scala
+++ b/core/shared/src/main/scala/fs2/Stream.scala
@@ -2102,6 +2102,30 @@ final class Stream[+F[_], +O] private[fs2] (private[fs2] val underlying: Pull[F,
   )(implicit F: Concurrent[F2]): Stream[F2, O2] =
     merge_(that) { case (s, fin) => s.onFinalize(fin) }
 
+  /** Like `mergeAndAwaitDownstream`, but halts as soon as _either_ branch halts. */
+  def mergeAndAwaitDownstreamHaltBoth[F2[x] >: F[x]: Concurrent, O2 >: O](
+      that: Stream[F2, O2]
+  ): Stream[F2, O2] =
+    noneTerminate.mergeAndAwaitDownstream(that.noneTerminate).unNoneTerminate
+
+  /** Like `mergeAndAwaitDownstream`, but halts as soon as the `s1` branch halts.
+    *
+    * Note: it is *not* guaranteed that the last element of the stream will come from `s1`.
+    */
+  def mergeAndAwaitDownstreamHaltL[F2[x] >: F[x]: Concurrent, O2 >: O](
+      that: Stream[F2, O2]
+  ): Stream[F2, O2] =
+    noneTerminate.mergeAndAwaitDownstream(that.map(Some(_))).unNoneTerminate
+
+  /** Like `mergeAndAwaitDownstream`, but halts as soon as the `s2` branch halts.
+    *
+    * Note: it is *not* guaranteed that the last element of the stream will come from `s2`.
+    */
+  def mergeAndAwaitDownstreamHaltR[F2[x] >: F[x]: Concurrent, O2 >: O](
+      that: Stream[F2, O2]
+  ): Stream[F2, O2] =
+    that.mergeAndAwaitDownstreamHaltL(this)
+
   /** Interleaves the two inputs nondeterministically. The output stream
     * halts after BOTH `s1` and `s2` terminate normally, or in the event
     * of an uncaught failure on either `s1` or `s2`. Has the property that