diff --git a/doc/requirements.txt b/doc/requirements.txt
index 9a48fc42..0404396a 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,9 +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.
-
 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
 sphinxcontrib-svg2pdfconverter>=0.1.0 # BSD
diff --git a/test-requirements.txt b/test-requirements.txt
index 13b903e2..9b91f1fa 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,6 +1,6 @@
 hacking>=6.1.0,<6.2.0 # Apache-2.0
 
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 flake8-import-order>=0.18.0,<0.19.0 # LGPLv3
 nodeenv>=0.9.4 # BSD
 testtools>=2.2.0 # MIT