diff --git a/doc/requirements.txt b/doc/requirements.txt
index ab289e81c60..6e8f4a0e154 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,7 +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.
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.2.0 # BSD
 sphinx_feature_classification>=1.0.0 # Apache-2.0
 openstackdocstheme>=2.2.1 # Apache-2.0
 oslotest>=3.2.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index cdf72fd136a..94ff22efc41 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,4 +1,4 @@
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 python-subunit>=1.0.0 # Apache-2.0/BSD
 testtools>=2.2.0 # MIT