diff --git a/httpx/_client.py b/httpx/_client.py
index 2b513b0d35..5e4c8e2713 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -51,6 +51,7 @@
     URLPattern,
     get_environment_proxies,
     get_logger,
+    is_https_redirect,
     same_origin,
 )
 
@@ -532,9 +533,10 @@ def _redirect_headers(self, request: Request, url: URL, method: str) -> Headers:
         headers = Headers(request.headers)
 
         if not same_origin(url, request.url):
-            # Strip Authorization headers when responses are redirected away from
-            # the origin.
-            headers.pop("Authorization", None)
+            if not is_https_redirect(request.url, url):
+                # Strip Authorization headers when responses are redirected
+                # away from the origin. (Except for direct HTTP to HTTPS redirects.)
+                headers.pop("Authorization", None)
 
             # Update the Host header.
             headers["Host"] = url.netloc.decode("ascii")
diff --git a/httpx/_utils.py b/httpx/_utils.py
index c92be8c8c0..4d791b0825 100644
--- a/httpx/_utils.py
+++ b/httpx/_utils.py
@@ -282,6 +282,21 @@ def same_origin(url: "URL", other: "URL") -> bool:
     )
 
 
+def is_https_redirect(url: "URL", location: "URL") -> bool:
+    """
+    Return 'True' if 'location' is a HTTPS upgrade of 'url'
+    """
+    if url.host != location.host:
+        return False
+
+    return (
+        url.scheme == "http"
+        and port_or_default(url) == 80
+        and location.scheme == "https"
+        and port_or_default(location) == 443
+    )
+
+
 def get_environment_proxies() -> typing.Dict[str, typing.Optional[str]]:
     """Gets proxy information from the environment"""
 
diff --git a/tests/client/test_redirects.py b/tests/client/test_redirects.py
index adc3aae388..ba02f0a288 100644
--- a/tests/client/test_redirects.py
+++ b/tests/client/test_redirects.py
@@ -270,6 +270,15 @@ def test_cross_domain_redirect_with_auth_header():
     assert "authorization" not in response.json()["headers"]
 
 
+def test_cross_domain_https_redirect_with_auth_header():
+    client = httpx.Client(transport=httpx.MockTransport(redirects))
+    url = "http://example.com/cross_domain"
+    headers = {"Authorization": "abc"}
+    response = client.get(url, headers=headers, follow_redirects=True)
+    assert response.url == "https://example.org/cross_domain_target"
+    assert "authorization" not in response.json()["headers"]
+
+
 def test_cross_domain_redirect_with_auth():
     client = httpx.Client(transport=httpx.MockTransport(redirects))
     url = "https://example.com/cross_domain"
@@ -287,6 +296,15 @@ def test_same_domain_redirect():
     assert response.json()["headers"]["authorization"] == "abc"
 
 
+def test_same_domain_https_redirect_with_auth_header():
+    client = httpx.Client(transport=httpx.MockTransport(redirects))
+    url = "http://example.org/cross_domain"
+    headers = {"Authorization": "abc"}
+    response = client.get(url, headers=headers, follow_redirects=True)
+    assert response.url == "https://example.org/cross_domain_target"
+    assert response.json()["headers"]["authorization"] == "abc"
+
+
 def test_body_redirect():
     """
     A 308 redirect should preserve the request body.
diff --git a/tests/test_utils.py b/tests/test_utils.py
index 88ef5877e9..e4bbb6ba2c 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -10,6 +10,7 @@
     get_ca_bundle_from_env,
     get_environment_proxies,
     guess_json_utf,
+    is_https_redirect,
     obfuscate_sensitive_headers,
     parse_header_links,
     same_origin,
@@ -221,6 +222,24 @@ def test_not_same_origin():
     assert not same_origin(origin1, origin2)
 
 
+def test_is_https_redirect():
+    url = httpx.URL("http://example.com")
+    location = httpx.URL("https://example.com")
+    assert is_https_redirect(url, location)
+
+
+def test_is_not_https_redirect():
+    url = httpx.URL("http://example.com")
+    location = httpx.URL("https://www.example.com")
+    assert not is_https_redirect(url, location)
+
+
+def test_is_not_https_redirect_if_not_default_ports():
+    url = httpx.URL("http://example.com:9999")
+    location = httpx.URL("https://example.com:1337")
+    assert not is_https_redirect(url, location)
+
+
 @pytest.mark.parametrize(
     ["pattern", "url", "expected"],
     [