diff --git a/src/JsonApi.php b/src/JsonApi.php
index d9debae..e7cf939 100644
--- a/src/JsonApi.php
+++ b/src/JsonApi.php
@@ -110,11 +110,17 @@ final class JsonApi implements RequestHandlerInterface
     {
         $header = $request->getHeaderLine('Accept');
 
-        if (empty($header) || $header === '*/*') {
+        if (empty($header)) {
             return;
         }
 
-        if ((new MediaTypes($header))->containsExactly(self::CONTENT_TYPE)) {
+        $mediaTypes = new MediaTypes($header);
+
+        if ($mediaTypes->containsExactly('*/*')) {
+            return;
+        }
+
+        if ($mediaTypes->containsExactly(self::CONTENT_TYPE)) {
             return;
         }
 
diff --git a/tests/specification/ContentNegotiationTest.php b/tests/specification/ContentNegotiationTest.php
index 655c344..3485f3e 100644
--- a/tests/specification/ContentNegotiationTest.php
+++ b/tests/specification/ContentNegotiationTest.php
@@ -48,7 +48,7 @@ class ContentNegotiationTest extends AbstractTestCase
         );
     }
 
-    public function test_error_when_valid_request_content_type_has_parameters()
+    public function test_error_when_request_content_type_has_parameters()
     {
         $request = $this->buildRequest('PATCH', '/users/1')
             ->withHeader('Content-Type', 'application/vnd.api+json;profile="http://example.com/last-modified"');
@@ -58,7 +58,7 @@ class ContentNegotiationTest extends AbstractTestCase
         $this->api->handle($request);
     }
 
-    public function test_error_when_all_valid_accepts_have_parameters()
+    public function test_error_when_all_accepts_have_parameters()
     {
         $request = $this->buildRequest('GET', '/users/1')
             ->withHeader('Accept', 'application/vnd.api+json;profile="http://example.com/last-modified", application/vnd.api+json;profile="http://example.com/versioning"');
@@ -77,4 +77,14 @@ class ContentNegotiationTest extends AbstractTestCase
 
         $this->assertEquals(200, $response->getStatusCode());
     }
+
+    public function test_success_when_accepts_wildcard()
+    {
+        $response = $this->api->handle(
+            $this->buildRequest('GET', '/users/1')
+                ->withHeader('Accept', '*/*')
+        );
+
+        $this->assertEquals(200, $response->getStatusCode());
+    }
 }