diff --git a/tests/constraints.txt b/tests/constraints.txt
index 5655ac2d3..3b30e6bb5 100644
--- a/tests/constraints.txt
+++ b/tests/constraints.txt
@@ -1 +1,8 @@
-Twisted!=18.4.0
\ No newline at end of file
+# Request the latest known version or newer of some dependencies to prevent the
+# pip dependency resolver from spending too much time backtracking.
+attrs>=20.2.0
+Pillow>=8.0.1
+pytest>=6.2.1
+pytest-twisted>=1.13.1
+sybil>=2.0.0
+Twisted>=19.10.0
diff --git a/tox.ini b/tox.ini
index d8e900e06..9908a4d51 100644
--- a/tox.ini
+++ b/tox.ini
@@ -67,7 +67,6 @@ commands =
 
 [pinned]
 deps =
-    -ctests/constraints.txt
     cryptography==2.0
     cssselect==0.9.1
     h2==3.2.0