diff --git a/acme/acme/client_test.py b/acme/acme/client_test.py
index 33ae3886b..b3d0f1921 100644
--- a/acme/acme/client_test.py
+++ b/acme/acme/client_test.py
@@ -707,6 +707,7 @@ class ClientTest(ClientTestBase):
             self.certr,
             self.rsn)
 
+
 class ClientV2Test(ClientTestBase):
     """Tests for acme.client.ClientV2."""
 
@@ -950,7 +951,6 @@ class ClientNetworkTest(unittest.TestCase):
         self.assertEqual(jws.signature.combined.kid, u'acct-uri')
         self.assertEqual(jws.signature.combined.url, u'url')
 
-
     def test_check_response_not_ok_jobj_no_error(self):
         self.response.ok = False
         self.response.json.return_value = {}
@@ -1113,8 +1113,8 @@ class ClientNetworkTest(unittest.TestCase):
 
         # Requests Library Exceptions
         except requests.exceptions.ConnectionError as z: #pragma: no cover
-            self.assertTrue("('Connection aborted.', error(111, 'Connection refused'))"
-                              == str(z) or "[WinError 10061]" in str(z))
+            self.assertTrue("'Connection aborted.'" in str(z) or "[WinError 10061]" in str(z))
+
 
 class ClientNetworkWithMockedResponseTest(unittest.TestCase):
     """Tests for acme.client.ClientNetwork which mock out response."""
diff --git a/acme/setup.py b/acme/setup.py
index 77ff7bae8..eac3974fa 100644
--- a/acme/setup.py
+++ b/acme/setup.py
@@ -9,15 +9,15 @@ version = '0.31.0.dev0'
 install_requires = [
     # load_pem_private/public_key (>=0.6)
     # rsa_recover_prime_factors (>=0.8)
-    'cryptography>=0.8',
+    'cryptography>=1.2.3',
     # formerly known as acme.jose:
     'josepy>=1.0.0',
     # Connection.set_tlsext_host_name (>=0.13)
     'mock',
-    'PyOpenSSL>=0.13',
+    'PyOpenSSL>=0.13.1',
     'pyrfc3339',
     'pytz',
-    'requests[security]>=2.4.1',  # security extras added in 2.4.1
+    'requests[security]>=2.6.0',  # security extras added in 2.4.1
     'requests-toolbelt>=0.3.0',
     'setuptools',
     'six>=1.9.0',  # needed for python_2_unicode_compatible
diff --git a/setup.py b/setup.py
index 2a9b2c203..9e6af2d4f 100644
--- a/setup.py
+++ b/setup.py
@@ -37,7 +37,7 @@ install_requires = [
     # in which we added 2.6 support (see #2243), so we relax the requirement.
     'ConfigArgParse>=0.9.3',
     'configobj',
-    'cryptography>=1.2',  # load_pem_x509_certificate
+    'cryptography>=1.2.3',  # load_pem_x509_certificate
     'josepy',
     'mock',
     'parsedatetime>=1.3',  # Calendar.parseDT
diff --git a/tools/oldest_constraints.txt b/tools/oldest_constraints.txt
index 80fce8b33..20fa0672a 100644
--- a/tools/oldest_constraints.txt
+++ b/tools/oldest_constraints.txt
@@ -37,13 +37,13 @@ pytz==2012rc0
 
 # Our setup.py constraints
 cloudflare==1.5.1
-cryptography==1.2.0
+cryptography==1.2.3
 google-api-python-client==1.5
 oauth2client==2.0
 parsedatetime==1.3
 pyparsing==1.5.5
 python-digitalocean==1.11
-requests[security]==2.4.1
+requests[security]==2.6.0
 
 # Ubuntu Xenial constraints
 ConfigArgParse==0.10.0