diff --git a/index.bs b/index.bs
index 931577114..1fb17decd 100644
--- a/index.bs
+++ b/index.bs
@@ -2201,6 +2201,14 @@ The following abstract operations operate on {{ReadableStream}} instances at a h
    1. If |reader| [=implements=] {{ReadableStreamBYOBReader}}, perform
       ! [$ReadableStreamBYOBReaderRelease$](|reader|).
    1. Otherwise, perform ! [$ReadableStreamDefaultReaderRelease$](|reader|).
+   1. Set |reader| to ! [$AcquireReadableStreamDefaultReader$](|source|).
+      <p class="note">The initial reader is released to ensure that any pending read requests
+      are immediately aborted, and no more chunks are pulled from |source|. A new reader is
+      acquired in order to keep |source| locked until the shutdown is [=finalized=], for example
+      to [=cancel a readable stream|cancel=] |source| if necessary.
+      This exchange of readers is not observable to author code and the user agent is free to
+      implement this differently, for example by keeping the same reader and internally aborting
+      its pending read requests.
    1. If |dest|.[=WritableStream/[[state]]=] is "`writable`" and !
       [$WritableStreamCloseQueuedOrInFlight$](|dest|) is false,
      1. If any [=chunks=] have been read but not yet written, write them to |dest|.
@@ -2216,6 +2224,7 @@ The following abstract operations operate on {{ReadableStream}} instances at a h
    1. If |reader| [=implements=] {{ReadableStreamBYOBReader}}, perform
       ! [$ReadableStreamBYOBReaderRelease$](|reader|).
    1. Otherwise, perform ! [$ReadableStreamDefaultReaderRelease$](|reader|).
+   1. Set |reader| to ! [$AcquireReadableStreamDefaultReader$](|source|).
    1. If |dest|.[=WritableStream/[[state]]=] is "`writable`" and !
       [$WritableStreamCloseQueuedOrInFlight$](|dest|) is false,
     1. If any [=chunks=] have been read but not yet written, write them to |dest|.
@@ -2224,8 +2233,10 @@ The following abstract operations operate on {{ReadableStream}} instances at a h
    1. [=Finalize=], passing along |error| if it was given.
   * <dfn id="rs-pipeTo-finalize"><i>Finalize</i></dfn>: both forms of shutdown will eventually ask
     to finalize, optionally with an error |error|, which means to perform the following steps:
-   1. Assert: |reader|.[=ReadableStreamGenericReader/[[stream]]=] is undefined.
    1. Perform ! [$WritableStreamDefaultWriterRelease$](|writer|).
+   1. If |reader| [=implements=] {{ReadableStreamBYOBReader}}, perform
+      ! [$ReadableStreamBYOBReaderRelease$](|reader|).
+   1. Otherwise, perform ! [$ReadableStreamDefaultReaderRelease$](|reader|).
    1. If |signal| is not undefined, [=AbortSignal/remove=] |abortAlgorithm| from |signal|.
    1. If |error| was given, [=reject=] |promise| with |error|.
    1. Otherwise, [=resolve=] |promise| with undefined.
diff --git a/reference-implementation/lib/abstract-ops/readable-streams.js b/reference-implementation/lib/abstract-ops/readable-streams.js
index 0b8613092..0973ce992 100644
--- a/reference-implementation/lib/abstract-ops/readable-streams.js
+++ b/reference-implementation/lib/abstract-ops/readable-streams.js
@@ -134,7 +134,7 @@ function ReadableStreamPipeTo(source, dest, preventClose, preventAbort, preventC
   assert(IsReadableStreamLocked(source) === false);
   assert(IsWritableStreamLocked(dest) === false);
 
-  const reader = AcquireReadableStreamDefaultReader(source);
+  let reader = AcquireReadableStreamDefaultReader(source);
   const writer = AcquireWritableStreamDefaultWriter(dest);
 
   source._disturbed = true;
@@ -315,6 +315,7 @@ function ReadableStreamPipeTo(source, dest, preventClose, preventAbort, preventC
       }
       shuttingDown = true;
       ReadableStreamDefaultReaderRelease(reader);
+      reader = AcquireReadableStreamDefaultReader(reader);
 
       if (dest._state === 'writable' && WritableStreamCloseQueuedOrInFlight(dest) === false) {
         uponFulfillment(waitForWritesToFinish(), () => finalize(isError, error));
@@ -324,8 +325,8 @@ function ReadableStreamPipeTo(source, dest, preventClose, preventAbort, preventC
     }
 
     function finalize(isError, error) {
-      assert(reader._stream === undefined);
       WritableStreamDefaultWriterRelease(writer);
+      ReadableStreamDefaultReaderRelease(reader);
 
       if (signal !== undefined) {
         signal.removeEventListener('abort', abortAlgorithm);