diff --git a/.github/workflows/tox.yml b/.github/workflows/tox.yml
index 280a7e5b..30f9f349 100644
--- a/.github/workflows/tox.yml
+++ b/.github/workflows/tox.yml
@@ -32,6 +32,8 @@ jobs:
         uses: actions/setup-python@v2
         with:
           python-version: ${{ matrix.python }}
+        env:
+          PIP_TRUSTED_HOST: "pypi.python.org pypi.org files.pythonhosted.org"
       - name: Install dependencies
         run: |
           sudo apt update
diff --git a/requirements.devel.txt b/requirements.devel.txt
index 5ea0a4f6..cea4f609 100644
--- a/requirements.devel.txt
+++ b/requirements.devel.txt
@@ -1 +1 @@
-tox==3.14.3
+tox==3.28.0
diff --git a/requirements.docs.txt b/requirements.docs.txt
index 8458faf2..7628b13e 100644
--- a/requirements.docs.txt
+++ b/requirements.docs.txt
@@ -1,4 +1 @@
-Sphinx==2.4.4
-docutils==0.16
-jinja2<3.1      # We need an older version due to compatilibility
-markupsafe<2.1  # Needed because of jinja2
+Sphinx==7.0.1
diff --git a/requirements.tests.txt b/requirements.tests.txt
index d36d68c7..809d8914 100644
--- a/requirements.tests.txt
+++ b/requirements.tests.txt
@@ -16,7 +16,8 @@ setuptools==44.0.0;python_version<"3.10"
 setuptools>64;python_version>="3.10"
 coverage==5.0.3;python_version<"3.10"
 coverage>=6;python_version>="3.10"
-flaky==3.6.1
+flaky==3.7.0;python_version<"3.6"
+flaky==3.8.1;python_version>="3.6"
 
 # for integration tests
 # eventlet is pinned until https://github.com/benoitc/gunicorn/pull/2581
diff --git a/setup.cfg b/setup.cfg
index 32977d4b..5e74955c 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -51,7 +51,9 @@ install_requires =
 	contextvars~=2.4;python_version>="3.5" and python_version<"3.7"
 
 [options.extras_require]
-gunicorn = gunicorn>=19.7.0
+gunicorn =
+	gunicorn>=19.7.0;python_version>"3.6"
+	gunicorn==19.7.0,<21.0;python_version>="3.5" and python_version<"3.8"
 raven = raven>=6.4.0
 celery =
 	celery~=4.4;python_version~="3.5.0"
diff --git a/setup.py b/setup.py
index 26576dbe..5668f57a 100644
--- a/setup.py
+++ b/setup.py
@@ -160,7 +160,8 @@
             'gevent>=20.9.0',
         ],
         gunicorn=[
-            'gunicorn>=19.7.0',
+            'gunicorn>=19.7.0;python_version>"3.6"',
+            'gunicorn>=19.7.0,<21.0;python_version>="3.5" and python_version<"3.8"',
         ],
         pg=[
             'sqlparse>=0.4.2',
diff --git a/tests/test_requests.py b/tests/test_requests.py
index 11f3448e..156e67dc 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -44,6 +44,15 @@
 import talisker.statsd
 import talisker.testing
 
+try:
+    # Compatible urllib3 HTTPResponses subclass their Base class.
+    URLLIB3_COMPATIBLE_VERSION = issubclass(
+        urllib3.response.HTTPResponse,
+        urllib3.response.BaseHTTPResponse
+    )
+except AttributeError:
+    URLLIB3_COMPATIBLE_VERSION = False
+
 
 def request(method='GET', host='http://example.com', url='/', **kwargs):
     req = requests.Request(method, url=host + url, **kwargs)
@@ -481,16 +490,36 @@ def set_responses(self, responses):
         self.response_iter = iter(responses)
 
     def make_response(self, content, status='200 OK', headers={}):
-        """Make a fake http.client.HTTPResponse based on a byte stream."""
+        """Make a fake HTTPResponse based on a byte stream.
+
+        For versions of urllib3 where urllib3.response.HTTPResponse is
+        not API-compatible with http.client.HTTPResponse, we return the
+        http.client version. For versions after, we return a
+        urllib3.response.HTTPResponse.
+        """
+        if not headers:
+            headers["Content-Type"] = "text/html"
+
         formatted_headers = '\r\n'.join(
             '{}: {}'.format(k, v) for k, v in headers.items()
         )
-        stream = 'HTTP/1.1 {}\r\n{}\r\n{}'.format(
+        stream = 'HTTP/1.1 {}\r\n{}\r\n\r\n{}'.format(
             status, formatted_headers, content,
         )
         sock = FakeSocket(stream.encode('utf8'))
-        response = http.client.HTTPResponse(sock)
-        response.begin()  # parse the stream
+        http_response = http.client.HTTPResponse(sock)
+        http_response.begin()
+
+        if not URLLIB3_COMPATIBLE_VERSION:
+            return http_response
+
+        response = urllib3.response.HTTPResponse(
+            body=http_response,
+            headers=headers,
+            status=http_response.status,
+            preload_content=False,
+            original_response=http_response,
+        )
         return response
 
     def make_request(self, pool, conn, method, url, **kwargs):
@@ -688,7 +717,8 @@ def test_adapter_exceptions_match_default(mock_urllib3, retry, response):
 
     exc = None
     try:
-        session.get('http://default/')
+        response = session.get('http://default/')
+        response.raise_for_status()
     except Exception as e:
         exc = e