diff --git a/doc/requirements.txt b/doc/requirements.txt
index fe166fd99..2ce339c25 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,9 +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>=2.2.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 reno>=3.1.0 # Apache-2.0
 
 # imported when the source code is parsed for generating documentation:
diff --git a/requirements.txt b/requirements.txt
index dee5ed99a..354397f19 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,12 +1,12 @@
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=2.0.0 # Apache-2.0
 
 futurist>=1.2.0 # Apache-2.0
 oslo.config>=5.2.0 # Apache-2.0
 oslo.context>=5.3.0 # Apache-2.0
 oslo.log>=3.36.0 # Apache-2.0
 oslo.utils>=3.37.0 # Apache-2.0
-oslo.serialization!=2.19.1,>=2.18.0 # Apache-2.0
-oslo.service!=1.28.1,>=1.24.0 # Apache-2.0
+oslo.serialization>=2.18.0 # Apache-2.0
+oslo.service>=1.24.0 # Apache-2.0
 stevedore>=1.20.0 # Apache-2.0
 debtcollector>=1.2.0 # Apache-2.0
 
diff --git a/test-requirements.txt b/test-requirements.txt
index 2b4fd0c2b..7c1b638df 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -12,10 +12,7 @@ pifpaf>=2.2.0 # Apache-2.0
 # for test_impl_kafka
 confluent-kafka>=1.3.0 # Apache-2.0
 
-# when we can require tox>= 1.4, this can go into tox.ini:
-#  [testenv:cover]
-#  deps = {[testenv]deps} coverage
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 
 # AMQP 1.0 support depends on the Qpid Proton AMQP 1.0
 # development libraries.