diff --git a/doc/requirements.txt b/doc/requirements.txt
index b5cc23e6f..87e359a55 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,7 +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.
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.1.1 # BSD
 openstackdocstheme>=2.2.0 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
 sphinxcontrib-apidoc>=0.2.0 # BSD
diff --git a/requirements.txt b/requirements.txt
index 2eec1a70d..88c0e2b6c 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,11 +2,11 @@
 # 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>=3.0.0 # Apache-2.0
 keystoneauth1>=3.5.0 # Apache-2.0
 iso8601>=0.1.11 # MIT
 oslo.i18n>=3.15.3 # 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>=0.7.2 # BSD
 stevedore>=2.0.1 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 7d4278a80..0c56a31a6 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,10 +1,10 @@
 hacking>=6.1.0,<6.2.0  # Apache-2.0
 bandit>=1.1.0 # 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
 python-keystoneclient>=3.8.0 # Apache-2.0
-python-cinderclient!=4.0.0,>=3.3.0 # Apache-2.0
+python-cinderclient>=4.0.1 # Apache-2.0
 python-glanceclient>=2.8.0 # Apache-2.0
 python-neutronclient>=6.7.0 # Apache-2.0
 requests-mock>=1.2.0 # Apache-2.0