diff --git a/doc/requirements.txt b/doc/requirements.txt
index 6fe7c34..12d5b68 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,4 +1,4 @@
 reno>=3.1.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.2.0 # BSD
 openstackdocstheme>=2.2.1 # Apache-2.0
 
diff --git a/requirements.txt b/requirements.txt
index 9423079..957f186 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,14 +1,10 @@
-# 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!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=3.0.0 # Apache-2.0
 neutron-lib>=1.25.0 # Apache-2.0
 oslo.config>=5.2.0 # Apache-2.0
 netaddr>=0.7.18 # BSD
 os-ken>=0.3.0 # 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
 packaging>=20.4  # Apache-2.0
 paramiko>=2.0.0 # LGPLv2.1+
@@ -16,5 +12,5 @@
 tenacity>=3.2.1 # Apache-2.0
 ddt>=1.0.1 # MIT
 testtools>=2.2.0 # MIT
-eventlet!=0.18.3,!=0.20.1,>=0.18.2 # MIT
+eventlet>=0.21.0 # MIT
 debtcollector>=1.2.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index f5bac7c..0151f21 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!=4.4,>=4.0 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 flake8-import-order==0.12 # LGPLv3
 python-subunit>=1.0.0 # Apache-2.0/BSD
 oslotest>=3.2.0 # Apache-2.0