diff --git a/storage/setup.py b/storage/setup.py
index 0c80684f6234..f0df696179d3 100644
--- a/storage/setup.py
+++ b/storage/setup.py
@@ -31,7 +31,7 @@
 dependencies = [
     "google-auth >= 1.2.0",
     "google-cloud-core >= 1.0.3, < 2.0dev",
-    "google-resumable-media >= 0.4.0",
+    "google-resumable-media >= 0.3.1, != 0.4.0, < 0.5dev",
 ]
 extras = {}
 
diff --git a/storage/tests/unit/test_blob.py b/storage/tests/unit/test_blob.py
index c3e94f19ef96..2bef097987dd 100644
--- a/storage/tests/unit/test_blob.py
+++ b/storage/tests/unit/test_blob.py
@@ -755,15 +755,13 @@ def test__get_download_url_on_the_fly_with_kms_key_name(self):
     @staticmethod
     def _mock_requests_response(status_code, headers, content=b"", stream=False):
         import requests
-        from urllib3.response import HTTPResponse
 
         response = requests.Response()
         response.status_code = status_code
         response.headers.update(headers)
         if stream:
-            raw = mock.create_autospec(HTTPResponse, instance=True)
+            raw = io.BytesIO(content)
             raw.headers = headers
-            raw.stream.return_value = iter([content])
             response.raw = raw
             response._content = False
         else:
@@ -816,12 +814,7 @@ def _check_session_mocks(self, client, transport, expected_url, headers=None):
         headers["range"] = "bytes=3-5"
         headers["accept-encoding"] = "gzip"
         call = mock.call(
-            "GET",
-            expected_url,
-            data=None,
-            headers=headers,
-            stream=True,
-            timeout=mock.ANY,
+            "GET", expected_url, data=None, headers=headers, timeout=mock.ANY
         )
         self.assertEqual(transport.request.mock_calls, [call, call])
 
@@ -916,12 +909,7 @@ def test__do_download_chunked(self):
         # ``headers`` was modified (in place) once for each API call.
         self.assertEqual(headers, {"range": "bytes=3-5"})
         call = mock.call(
-            "GET",
-            download_url,
-            data=None,
-            headers=headers,
-            stream=True,
-            timeout=mock.ANY,
+            "GET", download_url, data=None, headers=headers, timeout=mock.ANY
         )
         self.assertEqual(transport.request.mock_calls, [call, call])
 
@@ -949,12 +937,7 @@ def test__do_download_chunked_with_range(self):
         # ``headers`` was modified (in place) once for each API call.
         self.assertEqual(headers, {"range": "bytes=3-4"})
         call = mock.call(
-            "GET",
-            download_url,
-            data=None,
-            headers=headers,
-            stream=True,
-            timeout=mock.ANY,
+            "GET", download_url, data=None, headers=headers, timeout=mock.ANY
         )
         self.assertEqual(transport.request.mock_calls, [call, call])
 
@@ -1103,7 +1086,6 @@ def test_download_to_filename_wo_updated(self):
         self._download_to_filename_helper()
 
     def test_download_to_filename_corrupted(self):
-        from urllib3.response import HTTPResponse
         from google.resumable_media import DataCorruption
         from google.resumable_media.requests.download import _CHECKSUM_MISMATCH
 
@@ -1111,19 +1093,25 @@ def test_download_to_filename_corrupted(self):
         transport = mock.Mock(spec=["request"])
         empty_hash = base64.b64encode(hashlib.md5(b"").digest()).decode(u"utf-8")
         headers = {"x-goog-hash": "md5=" + empty_hash}
-        chunks = (b"noms1", b"coooookies2")
-        mock_raw = mock.create_autospec(HTTPResponse, instance=True)
-        mock_raw.headers = headers
-        mock_raw.stream.return_value = iter(chunks)
+        mock_raw = mock.Mock(headers=headers, spec=["headers"])
         response = mock.MagicMock(
             headers=headers,
             status_code=http_client.OK,
             raw=mock_raw,
-            spec=["__enter__", "__exit__", "headers", "status_code", "raw"],
+            spec=[
+                "__enter__",
+                "__exit__",
+                "headers",
+                "iter_content",
+                "status_code",
+                "raw",
+            ],
         )
         # i.e. context manager returns ``self``.
         response.__enter__.return_value = response
         response.__exit__.return_value = None
+        chunks = (b"noms1", b"coooookies2")
+        response.iter_content.return_value = iter(chunks)
 
         transport.request.return_value = response
         # Create a fake client/bucket and use them in the Blob() constructor.
@@ -1158,7 +1146,9 @@ def test_download_to_filename_corrupted(self):
         # Check the mocks.
         response.__enter__.assert_called_once_with()
         response.__exit__.assert_called_once_with(None, None, None)
-        mock_raw.stream.assert_called_once_with(8192, decode_content=False)
+        response.iter_content.assert_called_once_with(
+            chunk_size=8192, decode_unicode=False
+        )
         transport.request.assert_called_once_with(
             "GET",
             media_link,