diff --git a/docs/internals/contributing/writing-code/unit-tests.txt b/docs/internals/contributing/writing-code/unit-tests.txt
index 16f2939e9f..4fe32950cb 100644
--- a/docs/internals/contributing/writing-code/unit-tests.txt
+++ b/docs/internals/contributing/writing-code/unit-tests.txt
@@ -235,7 +235,7 @@ dependencies:
 *  geoip2_
 *  jinja2_ 2.7+
 *  numpy_
-*  Pillow_
+*  Pillow_ 4.2.0+
 *  PyYAML_
 *  pytz_ (required)
 *  pywatchman_
diff --git a/tests/files/tests.py b/tests/files/tests.py
index b50061649a..c60d69bf6a 100644
--- a/tests/files/tests.py
+++ b/tests/files/tests.py
@@ -17,9 +17,11 @@ from django.core.files.uploadedfile import (
 )
 
 try:
-    from PIL import Image
+    from PIL import Image, features
+    HAS_WEBP = features.check('webp')
 except ImportError:
     Image = None
+    HAS_WEBP = False
 else:
     from django.core.files import images
 
@@ -343,6 +345,7 @@ class GetImageDimensionsTests(unittest.TestCase):
                 size = images.get_image_dimensions(fh)
                 self.assertEqual(size, (None, None))
 
+    @unittest.skipUnless(HAS_WEBP, 'WEBP not installed')
     def test_webp(self):
         img_path = os.path.join(os.path.dirname(__file__), 'test.webp')
         with open(img_path, 'rb') as fh:
diff --git a/tests/requirements/py3.txt b/tests/requirements/py3.txt
index 5733df66e0..84a6bf0344 100644
--- a/tests/requirements/py3.txt
+++ b/tests/requirements/py3.txt
@@ -4,7 +4,7 @@ docutils
 geoip2 < 4.0.0
 jinja2 >= 2.9.2
 numpy
-Pillow != 5.4.0
+Pillow >=4.2.0, != 5.4.0
 # pylibmc/libmemcached can't be built on Windows.
 pylibmc; sys.platform != 'win32'
 python-memcached >= 1.59