diff --git a/requests/packages/urllib3/connectionpool.py b/requests/packages/urllib3/connectionpool.py
index 97da5446..26f01767 100644
--- a/requests/packages/urllib3/connectionpool.py
+++ b/requests/packages/urllib3/connectionpool.py
@@ -96,9 +96,17 @@ class VerifiedHTTPSConnection(HTTPSConnection):
 
         # Wrap socket using verification with the root certs in
         # trusted_root_certs
-        self.sock = ssl.wrap_socket(sock, self.key_file, self.cert_file,
-                                    cert_reqs=self.cert_reqs,
-                                    ca_certs=self.ca_certs)
+        try:
+          self.sock = ssl.wrap_socket(sock, self.key_file, self.cert_file,
+                                      cert_reqs=self.cert_reqs,
+                                      ca_certs=self.ca_certs,
+                                      ssl_version=ssl.PROTOCOL_SSLv3)
+        except ssl.SSLError:
+          self.sock = ssl.wrap_socket(sock, self.key_file, self.cert_file,
+                                      cert_reqs=self.cert_reqs,
+                                      ca_certs=self.ca_certs,
+                                      ssl_version=ssl.PROTOCOL_SSLv23)
+
         if self.ca_certs:
             match_hostname(self.sock.getpeercert(), self.host)