diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8d19ea86e..241443f2b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,11 @@
 
 Please refer to [UPGRADING](UPGRADING.md) guide for upgrading to a major version.
 
+## 7.4.4 - 2022-06-09
+
+* Fix failure to strip Authorization header on HTTP downgrade
+* Fix failure to strip the Cookie header on change in host or HTTP downgrade
+
 ## 7.4.3 - 2022-05-25
 
 * Fix cross-domain cookie leakage
diff --git a/src/RedirectMiddleware.php b/src/RedirectMiddleware.php
index 89c06526b..cedad4e77 100644
--- a/src/RedirectMiddleware.php
+++ b/src/RedirectMiddleware.php
@@ -142,7 +142,7 @@ static function (ResponseInterface $response) use ($uri, $statusCode) {
     }
 
     /**
-     * Check for too many redirects
+     * Check for too many redirects.
      *
      * @throws TooManyRedirectsException Too many redirects.
      */
@@ -178,7 +178,7 @@ public function modifyRequest(RequestInterface $request, array $options, Respons
             $modify['body'] = '';
         }
 
-        $uri = $this->redirectUri($request, $response, $protocols);
+        $uri = self::redirectUri($request, $response, $protocols);
         if (isset($options['idn_conversion']) && ($options['idn_conversion'] !== false)) {
             $idnOptions = ($options['idn_conversion'] === true) ? \IDNA_DEFAULT : $options['idn_conversion'];
             $uri = Utils::idnUriConvert($uri, $idnOptions);
@@ -198,19 +198,46 @@ public function modifyRequest(RequestInterface $request, array $options, Respons
             $modify['remove_headers'][] = 'Referer';
         }
 
-        // Remove Authorization header if host is different.
-        if ($request->getUri()->getHost() !== $modify['uri']->getHost()) {
+        // Remove Authorization and Cookie headers if required.
+        if (self::shouldStripSensitiveHeaders($request->getUri(), $modify['uri'])) {
             $modify['remove_headers'][] = 'Authorization';
+            $modify['remove_headers'][] = 'Cookie';
         }
 
         return Psr7\Utils::modifyRequest($request, $modify);
     }
 
     /**
-     * Set the appropriate URL on the request based on the location header
+     * Determine if we should strip sensitive headers from the request.
+     *
+     * We return true if either of the following conditions are true:
+     *
+     * 1. the host is different;
+     * 2. the scheme has changed, and now is non-https.
      */
-    private function redirectUri(RequestInterface $request, ResponseInterface $response, array $protocols): UriInterface
-    {
+    private static function shouldStripSensitiveHeaders(
+        UriInterface $originalUri,
+        UriInterface $modifiedUri
+    ): bool {
+        if (\strcasecmp($originalUri->getHost(), $modifiedUri->getHost()) !== 0) {
+            return true;
+        }
+
+        if ($originalUri->getScheme() !== $modifiedUri->getScheme() && 'https' !== $modifiedUri->getScheme()) {
+            return true;
+        }
+
+        return false;
+    }
+
+    /**
+     * Set the appropriate URL on the request based on the location header.
+     */
+    private static function redirectUri(
+        RequestInterface $request,
+        ResponseInterface $response,
+        array $protocols
+    ): UriInterface {
         $location = Psr7\UriResolver::resolve(
             $request->getUri(),
             new Psr7\Uri($response->getHeaderLine('Location'))
diff --git a/tests/RedirectMiddlewareTest.php b/tests/RedirectMiddlewareTest.php
index 1e0841a27..3378d241d 100644
--- a/tests/RedirectMiddlewareTest.php
+++ b/tests/RedirectMiddlewareTest.php
@@ -272,18 +272,37 @@ public function testInvokesOnRedirectForRedirects()
         self::assertTrue($call);
     }
 
-    public function testRemoveAuthorizationHeaderOnRedirect()
+    public function crossOriginRedirectProvider()
+    {
+        return [
+            ['http://example.com?a=b', 'http://test.com/', false],
+            ['https://example.com?a=b', 'https://test.com/', false],
+            ['http://example.com?a=b', 'https://test.com/', false],
+            ['https://example.com?a=b', 'http://test.com/', false],
+            ['http://example.com?a=b', 'http://example.com/', true],
+            ['https://example.com?a=b', 'https://example.com/', true],
+            ['http://example.com?a=b', 'https://example.com/', true],
+            ['https://example.com?a=b', 'http://example.com/', false],
+        ];
+    }
+
+    /**
+     * @dataProvider crossOriginRedirectProvider
+     */
+    public function testHeadersTreatmentOnRedirect($originalUri, $targetUri, $shouldBePresent)
     {
         $mock = new MockHandler([
-            new Response(302, ['Location' => 'http://test.com']),
-            static function (RequestInterface $request) {
-                self::assertFalse($request->hasHeader('Authorization'));
+            new Response(302, ['Location' => $targetUri]),
+            static function (RequestInterface $request) use ($shouldBePresent) {
+                self::assertSame($shouldBePresent, $request->hasHeader('Authorization'));
+                self::assertSame($shouldBePresent, $request->hasHeader('Cookie'));
+
                 return new Response(200);
             }
         ]);
         $handler = HandlerStack::create($mock);
         $client = new Client(['handler' => $handler]);
-        $client->get('http://example.com?a=b', ['auth' => ['testuser', 'testpass']]);
+        $client->get($originalUri, ['auth' => ['testuser', 'testpass'], 'headers' => ['Cookie' => 'foo=bar']]);
     }
 
     public function testNotRemoveAuthorizationHeaderOnRedirect()