diff --git a/doc/requirements.txt b/doc/requirements.txt
index b7e4e970e..6c96d9ac2 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,11 +1,7 @@
-# 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.
-
 # These are needed for docs generation
 openstackdocstheme>=2.2.1 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 sphinxcontrib-apidoc>=0.2.0  # BSD
 reno>=3.1.0 # Apache-2.0
-lxml!=3.7.0,>=3.4.1 # BSD
+lxml>=3.4.1 # BSD
 fixtures>=3.0.0 # Apache-2.0/BSD
diff --git a/requirements.txt b/requirements.txt
index 343c98f7e..1b69b9833 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,13 +1,13 @@
 # Requirements lower bounds listed here are our best effort to keep them up to
 # 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.
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=2.0.0 # Apache-2.0
 
 debtcollector>=1.2.0 # Apache-2.0
 keystoneauth1>=3.4.0 # Apache-2.0
 oslo.config>=5.2.0 # Apache-2.0
 oslo.i18n>=3.15.3 # Apache-2.0
-oslo.serialization!=2.19.1,>=2.18.0 # Apache-2.0
+oslo.serialization>=2.18.0 # Apache-2.0
 oslo.utils>=3.33.0 # Apache-2.0
 requests>=2.14.2 # Apache-2.0
 stevedore>=1.20.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index eb310e8d1..a88f20ac4 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,7 +1,7 @@
 hacking>=6.1.0,<6.2.0 # Apache-2.0
 flake8-docstrings==1.7.0 # MIT
 
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 keyring>=5.5.1 # MIT/PSF
 lxml>=4.5.0 # BSD
@@ -16,4 +16,4 @@ testscenarios>=0.4 # Apache-2.0/BSD
 testtools>=2.2.0 # MIT
 
 # Bandit security code scanner
-bandit!=1.6.0,>=1.1.0 # Apache-2.0
+bandit>=1.1.0 # Apache-2.0