diff --git a/doc/requirements.txt b/doc/requirements.txt
index 60ba4702..e85ec589 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,4 +1,4 @@
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>2.2.0 # BSD
 openstackdocstheme>=2.2.1 # Apache-2.0
 # releasenotes
 reno>=3.1.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index ccaa2e4b..16802fbb 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,10 +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>=2.0.0 # Apache-2.0
 eventlet>=0.26.1 # MIT
 msgpack>=1.0.0  # RPC library, BGP speaker(net_cntl)
diff --git a/test-requirements.txt b/test-requirements.txt
index f895baca..c9fa9aad 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,10 +1,6 @@
-# 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.
-
 hacking>=3.2.0,<3.3.0 # Apache-2.0
 
-coverage>=4.0,!=4.4 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 python-subunit>=1.0.0 # Apache-2.0/BSD
 oslotest>=3.2.0 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0