diff --git a/doc/requirements.txt b/doc/requirements.txt
index 64d6a3050..df520dd98 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,5 +1,5 @@
 doc8>=0.6.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 openstackdocstheme>=2.2.1 # 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 27d8e7e29..e7481c3eb 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,13 +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
-eventlet!=0.18.3,!=0.20.1,>=0.18.2 # MIT
+pbr>=2.0.0 # Apache-2.0
+eventlet>=0.18.2 # MIT
 netifaces>=0.10.4 # MIT
 oslo.config>=5.2.0 # Apache-2.0
 oslo.concurrency>=3.26.0 # Apache-2.0
 oslo.log>=4.6.1 # Apache-2.0
-oslo.service!=1.28.1,>=1.24.0 # Apache-2.0
+oslo.service>=1.24.0 # Apache-2.0
 oslo.utils>=3.34.0 # Apache-2.0
 Pint>=0.5 # BSD
 psutil>=3.2.2 # BSD
diff --git a/test-requirements.txt b/test-requirements.txt
index 339b33c09..a4f591f00 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.
-
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 testtools>=2.2.0 # MIT
 oslotest>=3.2.0 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0
-bandit!=1.6.0,>=1.1.0,<2.0.0 # Apache-2.0
+bandit>=1.1.0,<2.0.0 # Apache-2.0