diff --git a/doc/requirements.txt b/doc/requirements.txt
index 1fc85f4..e65b2dc 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,8 +1,4 @@
-# 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>=2.2.1 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 reno>=3.1.0 # Apache-2.0
 sphinxcontrib-httpdomain>=1.3.0 # BSD
diff --git a/test-requirements.txt b/test-requirements.txt
index f92585b..58d632b 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,4 +1,4 @@
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 # Hacking already pins down pep8, pyflakes and flake8
 hacking>=6.1.0,<6.2.0 # Apache-2.0