diff --git a/connexion/decorators/response.py b/connexion/decorators/response.py
index c278b6715..f1a9bcefc 100644
--- a/connexion/decorators/response.py
+++ b/connexion/decorators/response.py
@@ -55,9 +55,10 @@ def validate_response(self, data, status_code, headers, url):
                 raise NonConformingResponseBody(message=str(e))
 
         if response_definition and response_definition.get("headers"):
-            response_definition_header_keys = response_definition.get("headers").keys()
-            header_keys = headers.keys()
-            missing_keys = response_definition_header_keys - header_keys
+            required_header_keys = {k for (k, v) in response_definition.get("headers").items()
+                                    if v.get("required", False)}
+            header_keys = set(headers.keys())
+            missing_keys = required_header_keys - header_keys
             if missing_keys:
                 pretty_list = ', '.join(missing_keys)
                 msg = ("Keys in header don't match response specification. "
diff --git a/tests/api/test_headers.py b/tests/api/test_headers.py
index 0b6c88c75..0eb64ed63 100644
--- a/tests/api/test_headers.py
+++ b/tests/api/test_headers.py
@@ -17,8 +17,8 @@ def test_headers_produces(simple_app):
     assert response.headers["Location"] == "http://localhost/my/uri"
 
 
-def test_header_not_returned(simple_app):
-    app_client = simple_app.app.test_client()
+def test_header_not_returned(simple_openapi_app):
+    app_client = simple_openapi_app.app.test_client()
 
     response = app_client.post('/v1.0/goodday/noheader', data={})  # type: flask.Response
     assert response.status_code == 500  # view_func has not returned what was promised in spec
@@ -42,3 +42,10 @@ def test_no_content_object_and_have_headers(simple_app):
     resp = app_client.get('/v1.0/test-204-with-headers-nocontent-obj')
     assert resp.status_code == 204
     assert 'X-Something' in resp.headers
+
+
+def test_optional_header(simple_openapi_app):
+    app_client = simple_openapi_app.app.test_client()
+    resp = app_client.get('/v1.0/test-optional-headers')
+    assert resp.status_code == 200
+    assert 'X-Optional-Header' not in resp.headers
diff --git a/tests/fakeapi/hello/__init__.py b/tests/fakeapi/hello/__init__.py
index 26ef42e74..997c2ac0c 100644
--- a/tests/fakeapi/hello/__init__.py
+++ b/tests/fakeapi/hello/__init__.py
@@ -601,3 +601,7 @@ def get_date():
 
 def get_uuid():
     return {'value': uuid.UUID(hex='e7ff66d0-3ec2-4c4e-bed0-6e4723c24c51')}
+
+
+def test_optional_headers():
+    return {}, 200
diff --git a/tests/fixtures/simple/openapi.yaml b/tests/fixtures/simple/openapi.yaml
index 80a3bf4fc..a448830c6 100644
--- a/tests/fixtures/simple/openapi.yaml
+++ b/tests/fixtures/simple/openapi.yaml
@@ -690,6 +690,7 @@ paths:
               description: The URI of the created resource
               schema:
                 type: string
+              required: true
           content:
             'application/json':
               schema:
@@ -714,6 +715,7 @@ paths:
               description: The URI of the created resource
               schema:
                 type: string
+              required: true
           content:
             'application/json':
               schema:
@@ -731,6 +733,7 @@ paths:
               description: The URI of the created resource
               schema:
                 type: string
+              required: true
           content:
             text/plain:
               schema:
@@ -1140,6 +1143,22 @@ paths:
             application/json:
               schema:
                 type: object
+  /test-optional-headers:
+    get:
+      operationId: fakeapi.hello.test_optional_headers
+      responses:
+        '200':
+          description: Some object response
+          content:
+            application/json:
+              schema:
+                type: object
+          headers:
+            X-Optional-Header:
+              description: Optional header
+              schema:
+                type: string
+              required: false
 
 servers:
   - url: http://localhost:{port}/{basePath}
diff --git a/tests/fixtures/simple/swagger.yaml b/tests/fixtures/simple/swagger.yaml
index 32d680e60..de3db771e 100644
--- a/tests/fixtures/simple/swagger.yaml
+++ b/tests/fixtures/simple/swagger.yaml
@@ -556,21 +556,6 @@ paths:
           required: true
           type: string
 
-  /goodday/noheader:
-    post:
-      summary: Generate good day greeting
-      description: Generates a good day message.
-      operationId: fakeapi.hello.post_goodday_no_header
-      responses:
-        201:
-          description: gooday response
-          headers:
-            Location:
-              type: string
-              description: The URI of the created resource
-          schema:
-            type: object
-
   /goodevening/{name}:
     post:
       summary: Generate good evening