jsonapi.services.yml                 | 12 +++++-----
 src/Routing/EarlyFormatSetter.php    | 40 ++++++++++++++++++++++++++++++++
 src/StackMiddleware/FormatSetter.php | 44 ------------------------------------
 3 files changed, 46 insertions(+), 50 deletions(-)

diff --git a/jsonapi.services.yml b/jsonapi.services.yml
index fc9904b..87d93ce 100644
--- a/jsonapi.services.yml
+++ b/jsonapi.services.yml
@@ -150,13 +150,13 @@ services:
     # This way it can invalidate the data in here based on tags.
     tags: [{ name: cache.bin }]
 
-  # Middleware.
-  jsonapi.http_middleware.format_setter:
-    class: Drupal\jsonapi\StackMiddleware\FormatSetter
+  # Route filter.
+  jsonapi.route_filter.format_setter:
+    class: Drupal\jsonapi\Routing\EarlyFormatSetter
     tags:
-      # Set priority to 201 so it happens right before the page cache
-      # middleware (priority 200) has the opportunity to respond.
-      - { name: http_middleware, priority: 201 }
+      # Set to a high priority so it runs before content_type_header_matcher
+      # and other filters that might throw exceptions.
+      - { name: route_filter, priority: 100 }
 
   # Access Control
   jsonapi.entity_access_checker:
diff --git a/src/Routing/EarlyFormatSetter.php b/src/Routing/EarlyFormatSetter.php
new file mode 100644
index 0000000..61f714e
--- /dev/null
+++ b/src/Routing/EarlyFormatSetter.php
@@ -0,0 +1,40 @@
+<?php
+
+namespace Drupal\jsonapi\Routing;
+
+use Drupal\Core\Routing\RequestFormatRouteFilter;
+use Symfony\Component\HttpFoundation\Request;
+use Symfony\Component\Routing\RouteCollection;
+
+/**
+ * Sets the 'api_json' format for requests to JSON:API resources.
+ *
+ * Because this module places all JSON:API resources at paths prefixed with
+ * /jsonapi, and therefore not shared with other formats,
+ * \Drupal\Core\Routing\RequestFormatRouteFilter does correctly set the request
+ * format for those requests. However, it does so after other filters, such as
+ * \Drupal\Core\Routing\ContentTypeHeaderMatcher, run. If those other filters
+ * throw exceptions, we'd like the error response to be in JSON:API format as
+ * well, so we set that format here, in a higher priority (earlier running)
+ * filter. This works so long as the resource format can be determined before
+ * running any other filters, which is the case for JSON:API resources per
+ * above.
+ *
+ * @internal
+ */
+final class EarlyFormatSetter extends RequestFormatRouteFilter {
+
+  /**
+   * {@inheritdoc}
+   */
+  public function filter(RouteCollection $collection, Request $request) {
+    if (is_null($request->getRequestFormat(NULL))) {
+      $possible_formats = static::getAvailableFormats($collection);
+      if ($possible_formats === ['api_json']) {
+        $request->setRequestFormat('api_json');
+      }
+    }
+    return $collection;
+  }
+
+}
diff --git a/src/StackMiddleware/FormatSetter.php b/src/StackMiddleware/FormatSetter.php
deleted file mode 100644
index 4896e9e..0000000
--- a/src/StackMiddleware/FormatSetter.php
+++ /dev/null
@@ -1,44 +0,0 @@
-<?php
-
-namespace Drupal\jsonapi\StackMiddleware;
-
-use Symfony\Component\HttpFoundation\AcceptHeader;
-use Symfony\Component\HttpFoundation\Request;
-use Symfony\Component\HttpKernel\HttpKernelInterface;
-
-/**
- * Sets the 'api_json' for requests with a JSON:API Content-Type header.
- *
- * @internal
- */
-final class FormatSetter implements HttpKernelInterface {
-
-  /**
-   * The wrapped HTTP kernel.
-   *
-   * @var \Symfony\Component\HttpKernel\HttpKernelInterface
-   */
-  protected $httpKernel;
-
-  /**
-   * Constructs a FormatSetter object.
-   *
-   * @param \Symfony\Component\HttpKernel\HttpKernelInterface $http_kernel
-   *   The decorated kernel.
-   */
-  public function __construct(HttpKernelInterface $http_kernel) {
-    $this->httpKernel = $http_kernel;
-  }
-
-  /**
-   * {@inheritdoc}
-   */
-  public function handle(Request $request, $type = self::MASTER_REQUEST, $catch = TRUE) {
-    $accepted = AcceptHeader::fromString($request->headers->get('Accept'));
-    if ($accepted->get('application/vnd.api+json')) {
-      $request->setRequestFormat('api_json');
-    }
-    return $this->httpKernel->handle($request, $type, $catch);
-  }
-
-}