diff --git a/doc/requirements.txt b/doc/requirements.txt
index f9081ab67..566c47fc4 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,8 +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>=2.1.1 # BSD
 reno>=3.1.0 # Apache-2.0
 sphinxcontrib-programoutput>=0.11  # BSD
 python-openstackclient>=3.12.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index 283aab0ca..ca78e2b6f 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,21 +2,17 @@
 # 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 should be first
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=3.0.0 # Apache-2.0
 
 oslo.config>=5.2.0 # Apache-2.0
 oslo.log>=3.36.0 # Apache-2.0
-oslo.serialization!=2.19.1,>=2.18.0 # Apache-2.0
+oslo.serialization>=2.20.0 # Apache-2.0
 oslo.utils>=3.33.0 # Apache-2.0
 PrettyTable>=0.7.1 # BSD
 requests>=2.14.2 # Apache-2.0
 simplejson>=3.5.1 # MIT
-Babel!=2.4.0,>=2.3.4 # BSD
+Babel>=2.5.0 # BSD
 osc-lib>=1.10.0 # Apache-2.0
 python-keystoneclient>=3.8.0 # Apache-2.0
 debtcollector>=1.2.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index aae70c7b6..ea299aedc 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>=4.4.1 # Apache-2.0
 ddt>=1.0.1 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 stestr>=2.0.0 # Apache-2.0