diff --git a/requirements.txt b/requirements.txt
index 917c31a..126cbe4 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,6 +1,6 @@
 coverage==3.6.0
-requests==2.1.0
-requests_oauthlib==0.4.0
+requests>=2.1.0
+requests_oauthlib>=0.4.0
 python-coveralls==2.1.0
 nose-cov==1.6
-responses==0.2.0
+responses==0.3.0
diff --git a/setup.py b/setup.py
index 09ea8ec..e203cc9 100755
--- a/setup.py
+++ b/setup.py
@@ -23,7 +23,7 @@
 setup(
     name='twython',
     version=__version__,
-    install_requires=['requests2.1.0', 'requests_oauthlib==0.4.0'],
+    install_requires=['requests>=2.1.0', 'requests_oauthlib>=0.4.0'],
     author='Ryan McGrath',
     author_email='ryan@venodesigns.net',
     license=open('LICENSE').read(),
diff --git a/tests/test_core.py b/tests/test_core.py
index 98d3a47..1aa0eea 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -262,16 +262,16 @@ def test_get_lastfunction_header_should_return_header(self):
         """Test getting last specific header of the last API call works"""
         endpoint = 'statuses/home_timeline'
         url = self.get_url(endpoint)
-        self.register_response(responses.GET, url, adding_headers={'x-rate-limit-remaining': 37})
+        self.register_response(responses.GET, url, adding_headers={'x-rate-limit-remaining': '37'})
 
         self.api.get(endpoint)
 
         value = self.api.get_lastfunction_header('x-rate-limit-remaining')
-        self.assertEqual(37, value)
+        self.assertEqual('37', value)
         value2 = self.api.get_lastfunction_header('does-not-exist')
         self.assertIsNone(value2)
-        value3 = self.api.get_lastfunction_header('not-there-either', 96)
-        self.assertEqual(96, value3)
+        value3 = self.api.get_lastfunction_header('not-there-either', '96')
+        self.assertEqual('96', value3)
 
     def test_get_lastfunction_header_should_raise_error_when_no_previous_call(self):
         """Test attempting to get a header when no API call was made raises a TwythonError"""
@@ -286,7 +286,7 @@ def test_sends_correct_accept_encoding_header(self):
 
         self.api.get(endpoint)
 
-        self.assertEqual(b'gzip, deflate, compress', responses.calls[0].request.headers['Accept-Encoding'])
+        self.assertEqual(b'gzip, deflate', responses.calls[0].request.headers['Accept-Encoding'])
 
     # Static methods
     def test_construct_api_url(self):