diff --git a/doc/requirements.txt b/doc/requirements.txt
index 1489bcee5..10d3b9fba 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,3 +1,3 @@
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.1.1 # BSD
 openstackdocstheme>=2.2.1 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index dac35ac52..07efe845d 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,9 +2,6 @@
 # date but we do not test them so no guarantee of having them all correct. If
 # you find any incorrect lower bounds, let us know or propose a fix.
 
-# 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.
 pbr>=4.0.0 # Apache-2.0
 
 Jinja2>=2.10 # BSD License (3 clause)
diff --git a/test-requirements.txt b/test-requirements.txt
index bddbc8133..898aa0ec2 100644
--- a/test-requirements.txt
+++ b/test-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.
-
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 testtools>=2.2.0 # MIT
 oslotest>=3.2.0 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0