diff --git a/core/shared/src/main/scala/fs2/Pull.scala b/core/shared/src/main/scala/fs2/Pull.scala
index 16f86cbde3..ed7c5f4df8 100644
--- a/core/shared/src/main/scala/fs2/Pull.scala
+++ b/core/shared/src/main/scala/fs2/Pull.scala
@@ -321,6 +321,16 @@ object Pull extends PullLowPriority {
       * Use `p.void.stream` to explicitly ignore the result of a pull.
       */
     def streamNoScope: Stream[F, O] = new Stream(self)
+
+    private[fs2] def flatMapOutput[F2[x] >: F[x], O2](
+      f: O => Pull[F2, O2, Unit]
+    ): Pull[F2, O2, Unit] =
+      self match {
+        case a: AlgEffect[F, Unit] => a
+        case r: Terminal[_]        => r
+        case _                     => FlatMapOutput(self, f)
+    }
+
   }
 
   private[this] val unit: Terminal[Unit] = Succeeded(())
@@ -1029,7 +1039,7 @@ object Pull extends PullLowPriority {
           else {
             def go(idx: Int): Pull[G, X, Unit] =
               if (idx == chunk.size)
-                flatMapOutput[G, G, Y, X](tail, fun)
+                tail.flatMapOutput(fun)
               else {
                 try {
                   var j = idx
@@ -1046,8 +1056,7 @@ object Pull extends PullLowPriority {
                     case Succeeded(_) => go(j + 1)
                     case Fail(err)    => Fail(err)
                     case interruption @ Interrupted(_, _) =>
-                      val ib = interruptBoundary(tail, interruption)
-                      flatMapOutput[G, G, Y, X](ib, fun)
+                      interruptBoundary(tail, interruption).flatMapOutput(fun)
                   }
                 } catch { case NonFatal(e) => Fail(e) }
               }
@@ -1288,16 +1297,6 @@ object Pull extends PullLowPriority {
     go(initScope, None, initFk, new OuterRun(init), stream)
   }
 
-  private[fs2] def flatMapOutput[F[_], F2[x] >: F[x], O, O2](
-      p: Pull[F, O, Unit],
-      f: O => Pull[F2, O2, Unit]
-  ): Pull[F2, O2, Unit] =
-    p match {
-      case a: AlgEffect[F, Unit] => a
-      case r: Terminal[_]        => r
-      case _                     => FlatMapOutput(p, f)
-    }
-
   private[fs2] def translate[F[_], G[_], O](
       stream: Pull[F, O, Unit],
       fK: F ~> G
diff --git a/core/shared/src/main/scala/fs2/Stream.scala b/core/shared/src/main/scala/fs2/Stream.scala
index 57609af1ce..d4a7eb6994 100644
--- a/core/shared/src/main/scala/fs2/Stream.scala
+++ b/core/shared/src/main/scala/fs2/Stream.scala
@@ -962,6 +962,8 @@ final class Stream[+F[_], +O] private[fs2] (private[fs2] val underlying: Pull[F,
       queue: Queue[F2, Option[Chunk[O2]]]
   ): Stream[F2, Nothing] = enqueueNoneTerminatedChunks(queue: QueueSink[F2, Option[Chunk[O2]]])
 
+  import Pull.StreamPullOps
+
   /** Alias for `flatMap(o => Stream.eval(f(o)))`.
     *
     * @example {{{
@@ -975,8 +977,8 @@ final class Stream[+F[_], +O] private[fs2] (private[fs2] val underlying: Pull[F,
     * is available, however, with caveats.
     */
   def evalMap[F2[x] >: F[x], O2](f: O => F2[O2]): Stream[F2, O2] = {
-    def evalOut(o: O): Pull[F2, O2, Unit] = Pull.eval(f(o)).flatMap(Pull.output1)
-    Pull.flatMapOutput[F, F2, O, O2](underlying, evalOut).streamNoScope
+    def evalOut(o: O) = Pull.eval(f(o)).flatMap(Pull.output1)
+    underlying.flatMapOutput(evalOut).streamNoScope
   }
 
   /** Like `evalMap`, but operates on chunks for performance. This means this operator
@@ -1194,7 +1196,7 @@ final class Stream[+F[_], +O] private[fs2] (private[fs2] val underlying: Pull[F,
   def flatMap[F2[x] >: F[x], O2](
       f: O => Stream[F2, O2]
   )(implicit ev: NotGiven[O <:< Nothing]): Stream[F2, O2] =
-    new Stream(Pull.flatMapOutput[F, F2, O, O2](underlying, (o: O) => f(o).underlying))
+    underlying.flatMapOutput((o: O) => f(o).underlying).streamNoScope
 
   /** Alias for `flatMap(_ => s2)`. */
   def >>[F2[x] >: F[x], O2](
@@ -1286,8 +1288,7 @@ final class Stream[+F[_], +O] private[fs2] (private[fs2] val underlying: Pull[F,
     * }}}
     */
   def foreach[F2[x] >: F[x]](f: O => F2[Unit]): Stream[F2, Nothing] = {
-    def exec(o: O): Pull[F2, Nothing, Unit] = Pull.eval(f(o))
-    Pull.flatMapOutput[F, F2, O, Nothing](underlying, exec).streamNoScope
+    underlying.flatMapOutput(o => Pull.eval(f(o))).streamNoScope
   }
 
   /** Partitions the input into a stream of chunks according to a discriminator function.