diff --git a/doc/requirements.txt b/doc/requirements.txt
index 1a5b4da..79f2552 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,8 +1,5 @@
-# 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.
 fixtures>=3.0.0 # Apache-2.0/BSD
 openstackdocstheme>=2.2.1 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 sphinxcontrib-apidoc>=0.2.0  # BSD
diff --git a/test-requirements.txt b/test-requirements.txt
index 80915d5..9e7302d 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -3,7 +3,7 @@ hacking>=6.1.0,<6.2.0 # Apache-2.0
 oslotest>=3.2.0 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0
 
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 
 # Bandit security code scanner
 bandit>=1.7.0,<1.8.0 # Apache-2.0