diff --git a/doc/requirements.txt b/doc/requirements.txt
index fd4b2b67..1351241b 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,7 +1,3 @@
-# The order of packages is significant, because pip processes them in the order
-# of appearance. Changing the order has an impact on the overall integration
-# process, which may cause wedges in the gate later.
-
 openstackdocstheme>=2.2.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 reno>=3.1.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 17861a03..2cff2d31 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -3,4 +3,4 @@ oslotest>=3.2.0 # Apache-2.0
 requests>=2.14.2 # Apache-2.0
 stestr>=2.0.0 # Apache-2.0
 
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0