diff --git a/requests/sessions.py b/requests/sessions.py

index ef3f22b..a0a23ee 100644

--- a/requests/sessions.py

+++ b/requests/sessions.py

@@ -89,6 +89,23 @@ def merge_hooks(request_hooks, session_hooks, dict_class=OrderedDict):

 class SessionRedirectMixin(object):

+

+    def should_strip_auth(self, old_url, new_url):

+        """Decide whether Authorization header should be removed when redirecting"""

+        old_parsed = urlparse(old_url)

+        new_parsed = urlparse(new_url)

+        if old_parsed.hostname != new_parsed.hostname:

+            return True

+        # Special case: allow http -> https redirect when using the standard

+        # ports. This isn't specified by RFC 7235, but is kept to avoid

+        # breaking backwards compatibility with older versions of requests

+        # that allowed any redirects on the same host.

+        if (old_parsed.scheme == 'http' and old_parsed.port in (80, None)

+                and new_parsed.scheme == 'https' and new_parsed.port in (443, None)):

+            return False

+        # Standard case: root URI must match

+        return old_parsed.port != new_parsed.port or old_parsed.scheme != new_parsed.scheme

+

     def resolve_redirects(self, resp, req, stream=False, timeout=None,

                           verify=True, cert=None, proxies=None):

         """Receives a Response. Returns a generator of Responses."""

@@ -209,14 +226,10 @@ class SessionRedirectMixin(object):

         headers = prepared_request.headers

         url = prepared_request.url

-        if 'Authorization' in headers:

+        if 'Authorization' in headers and self.should_strip_auth(response.request.url, url):

             # If we get redirected to a new host, we should strip out any

             # authentication headers.

-            original_parsed = urlparse(response.request.url)

-            redirect_parsed = urlparse(url)

-

-            if (original_parsed.hostname != redirect_parsed.hostname):

-                del headers['Authorization']

+            del headers['Authorization']

         # .netrc might have more auth for us on our new host.

         new_auth = get_netrc_auth(url) if self.trust_env else None

diff --git a/test_requests.py b/test_requests.py

index 15406a2..e19b436 100755

--- a/test_requests.py

+++ b/test_requests.py

@@ -991,6 +991,27 @@ class RequestsTestCase(unittest.TestCase):

         assert h1 == h2

+    def test_should_strip_auth_host_change(self):

+        s = requests.Session()

+        assert s.should_strip_auth('http://example.com/foo', 'http://another.example.com/')

+

+    def test_should_strip_auth_http_downgrade(self):

+        s = requests.Session()

+        assert s.should_strip_auth('https://example.com/foo', 'http://example.com/bar')

+

+    def test_should_strip_auth_https_upgrade(self):

+        s = requests.Session()

+        assert not s.should_strip_auth('http://example.com/foo', 'https://example.com/bar')

+        assert not s.should_strip_auth('http://example.com:80/foo', 'https://example.com/bar')

+        assert not s.should_strip_auth('http://example.com/foo', 'https://example.com:443/bar')

+        # Non-standard ports should trigger stripping

+        assert s.should_strip_auth('http://example.com:8080/foo', 'https://example.com/bar')

+        assert s.should_strip_auth('http://example.com/foo', 'https://example.com:8443/bar')

+

+    def test_should_strip_auth_port_change(self):

+        s = requests.Session()

+        assert s.should_strip_auth('http://example.com:1234/foo', 'https://example.com:4321/bar')

+

     def test_manual_redirect_with_partial_body_read(self):

         s = requests.Session()

         r1 = s.get(httpbin('redirect/2'), allow_redirects=False, stream=True)