diff --git a/aiohttp/protocol.py b/aiohttp/protocol.py
index 4663d1edd5e..6eb63b651ad 100644
--- a/aiohttp/protocol.py
+++ b/aiohttp/protocol.py
@@ -521,8 +521,6 @@ class HttpMessage:
     # this is useful for wsgi's start_response implementation.
     _send_headers = False
 
-    _has_user_agent = False
-
     def __init__(self, transport, version, close):
         self.transport = transport
         self.version = version
@@ -595,9 +593,6 @@ def add_header(self, name, value):
             self.chunked = value.lower().strip() == 'chunked'
 
         elif name not in self.HOP_HEADERS:
-            if name == 'USER-AGENT':
-                self._has_user_agent = True
-
             # ignore hop-by-hop headers
             self.headers.add(name, value)
 
@@ -805,8 +800,6 @@ class Response(HttpMessage):
         'TRAILERS',
         'TRANSFER-ENCODING',
         'UPGRADE',
-        'SERVER',
-        'DATE',
     }
 
     @staticmethod
@@ -833,8 +826,10 @@ def __init__(self, transport, status,
     def _add_default_headers(self):
         super()._add_default_headers()
 
-        self.headers.extend((('DATE', format_date_time(None)),
-                             ('SERVER', self.SERVER_SOFTWARE),))
+        if 'DATE' not in self.headers:
+            # format_date_time(None) is quite expensive
+            self.headers.setdefault('DATE', format_date_time(None))
+        self.headers.setdefault('SERVER', self.SERVER_SOFTWARE)
 
 
 class Request(HttpMessage):
@@ -853,5 +848,4 @@ def __init__(self, transport, method, path,
     def _add_default_headers(self):
         super()._add_default_headers()
 
-        if not self._has_user_agent:
-            self.headers['USER-AGENT'] = self.SERVER_SOFTWARE
+        self.headers.setdefault('USER-AGENT', self.SERVER_SOFTWARE)
diff --git a/tests/test_http_protocol.py b/tests/test_http_protocol.py
index 96c04c8d1bb..c4bfca4b2f4 100644
--- a/tests/test_http_protocol.py
+++ b/tests/test_http_protocol.py
@@ -479,3 +479,18 @@ def test_write_drain(self):
 
         res = msg.write(b'1')
         self.assertEqual(res, ())
+
+    def test_dont_override_request_headers_with_default_values(self):
+        msg = protocol.Request(
+            self.transport, 'GET', '/index.html', close=True)
+        msg.add_header('USER-AGENT', 'custom')
+        msg._add_default_headers()
+        self.assertEqual('custom', msg.headers['USER-AGENT'])
+
+    def test_dont_override_response_headers_with_default_values(self):
+        msg = protocol.Response(self.transport, 200, http_version=(1, 0))
+        msg.add_header('DATE', 'now')
+        msg.add_header('SERVER', 'custom')
+        msg._add_default_headers()
+        self.assertEqual('custom', msg.headers['SERVER'])
+        self.assertEqual('now', msg.headers['DATE'])