.../big_pipe/src/Render/BigPipeResponse.php        |  3 +-
 ...cheableStreamedResponseEventDispatcherTrait.php |  2 +-
 .../page_cache/src/StackMiddleware/PageCache.php   | 57 +++++++++++++---------
 3 files changed, 37 insertions(+), 25 deletions(-)

diff --git a/core/modules/big_pipe/src/Render/BigPipeResponse.php b/core/modules/big_pipe/src/Render/BigPipeResponse.php
index 2987499..1132fe2 100644
--- a/core/modules/big_pipe/src/Render/BigPipeResponse.php
+++ b/core/modules/big_pipe/src/Render/BigPipeResponse.php
@@ -2,9 +2,8 @@
 
 namespace Drupal\big_pipe\Render;
 
-use Drupal\Core\Render\HtmlResponse;
-use Drupal\Core\Render\CacheableStreamedResponseEventDispatcherTrait;
 use Drupal\Core\Render\CacheableStreamedResponseInterface;
+use Drupal\Core\Render\HtmlResponse;
 
 /**
  * A response that is sent in chunks by the BigPipe service.
diff --git a/core/lib/Drupal/Core/Render/CacheableStreamedResponseEventDispatcherTrait.php b/core/modules/big_pipe/src/Render/CacheableStreamedResponseEventDispatcherTrait.php
similarity index 98%
rename from core/lib/Drupal/Core/Render/CacheableStreamedResponseEventDispatcherTrait.php
rename to core/modules/big_pipe/src/Render/CacheableStreamedResponseEventDispatcherTrait.php
index 2cd820b..9a5a073 100644
--- a/core/lib/Drupal/Core/Render/CacheableStreamedResponseEventDispatcherTrait.php
+++ b/core/modules/big_pipe/src/Render/CacheableStreamedResponseEventDispatcherTrait.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\Core\Render;
+namespace Drupal\big_pipe\Render;
 
 use Drupal\Core\Cache\CacheableResponseInterface;
 use Symfony\Component\HttpKernel\Event\FilterResponseEvent;
diff --git a/core/modules/page_cache/src/StackMiddleware/PageCache.php b/core/modules/page_cache/src/StackMiddleware/PageCache.php
index fc73ac0..c8b1fcf 100644
--- a/core/modules/page_cache/src/StackMiddleware/PageCache.php
+++ b/core/modules/page_cache/src/StackMiddleware/PageCache.php
@@ -94,6 +94,11 @@ public function terminate(Request $request, Response $response) {
         $this->storeResponse($request, $streamed_response);
       }
     }
+
+    // Delegate, per https://github.com/stackphp/builder/issues/14.
+    if ($this->httpKernel instanceof TerminableInterface) {
+      $this->httpKernel->terminate($request, $response);
+    }
   }
 
   /**
@@ -221,31 +226,25 @@ protected function fetch(Request $request, $type = self::MASTER_REQUEST, $catch
     /** @var \Symfony\Component\HttpFoundation\Response $response */
     $response = $this->httpKernel->handle($request, $type, $catch);
 
-    // Currently it is not possible to cache binary file or streamed responses:
-    // https://github.com/symfony/symfony/issues/9128#issuecomment-25088678.
-    // Therefore exclude them, even for subclasses that implement
-    // CacheableResponseInterface.
-    if ($response instanceof BinaryFileResponse || $response instanceof StreamedResponse) {
-      return $response;
-    }
-    // The exception: streamed responses that implement
-    // StreamedResponseInterface: those can be cached by PageCache during the
-    // 'terminate' phase/event. Already set the 'X-Drupal-Cache' header, so that
-    // header is present as expected.
+    // The storing of cacheable streamed responses is deferred to terminate().
+    // The 'X-Drupal-Cache' header must be set here however, since the response
+    // is already sent to the client before terminate() is called.
     // @see ::terminate()
-    elseif ($response instanceof CacheableStreamedResponseInterface) {
-      // Mark response as a cache miss.
-      $response->headers->set('X-Drupal-Cache', 'MISS');
+    if ($response instanceof CacheableStreamedResponseInterface) {
+      // Mark streamed response as a cache miss, but only if caching is allowed
+      // for this streamed response.
+      if ($this->responsePolicy->check($response, $request) !== ResponsePolicyInterface::DENY) {
+        $response->headers->set('X-Drupal-Cache', 'MISS');
+      }
       return $response;
     }
 
-    // Allow policy rules to further restrict which responses to cache.
-    if ($this->responsePolicy->check($response, $request) === ResponsePolicyInterface::DENY) {
-      return $response;
+    // Only set the 'X-Drupal-Cache' header if caching is allowed for this
+    // response.
+    if ($this->storeResponse($request, $response)) {
+      $response->headers->set('X-Drupal-Cache', 'MISS');
     }
 
-    $this->storeResponse($request, $response);
-
     return $response;
   }
 
@@ -256,6 +255,8 @@ protected function fetch(Request $request, $type = self::MASTER_REQUEST, $catch
    *   A request object.
    * @param \Symfony\Component\HttpFoundation\Response $response
    *   A response object that should be stored in the page cache.
+   *
+   * @returns bool
    */
   protected function storeResponse(Request $request, Response $response) {
     // Drupal's primary cache invalidation architecture is cache tags: any
@@ -280,7 +281,20 @@ protected function storeResponse(Request $request, Response $response) {
     //   so by replacing/extending this middleware service or adding another
     //   one.
     if (!$response instanceof CacheableResponseInterface) {
-      return;
+      return FALSE;
+    }
+
+    // Currently it is not possible to cache binary file or streamed responses:
+    // https://github.com/symfony/symfony/issues/9128#issuecomment-25088678.
+    // Therefore exclude them, even for subclasses that implement
+    // CacheableResponseInterface.
+    if ($response instanceof BinaryFileResponse || $response instanceof StreamedResponse) {
+      return FALSE;
+    }
+
+    // Allow policy rules to further restrict which responses to cache.
+    if ($this->responsePolicy->check($response, $request) === ResponsePolicyInterface::DENY) {
+      return FALSE;
     }
 
     $request_time = $request->server->get('REQUEST_TIME');
@@ -312,8 +326,7 @@ protected function storeResponse(Request $request, Response $response) {
       $this->set($request, $response, $expire, $tags);
     }
 
-    // Mark response as a cache miss.
-    $response->headers->set('X-Drupal-Cache', 'MISS');
+    return TRUE;
   }
 
   /**