diff --git a/doc/requirements.txt b/doc/requirements.txt
index 5984ff01e..1f0df18c5 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>=2.0.0 # BSD
 openstackdocstheme>=2.2.1 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
 doc8>=0.6.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index a8cb2f147..3943b9c44 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,5 @@
 # See: https://bugs.launchpad.net/pbr/+bug/1384919 for why this is here...
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=2.0.0 # Apache-2.0
 
 # Packages needed for using this library.
 
@@ -23,7 +23,7 @@ automaton>=1.9.0 # Apache-2.0
 
 # For common utilities
 oslo.utils>=3.33.0 # Apache-2.0
-oslo.serialization!=2.19.1,>=2.18.0 # Apache-2.0
+oslo.serialization>=2.18.0 # Apache-2.0
 tenacity>=6.0.0 # Apache-2.0
 
 # For lru caches and such
diff --git a/setup.cfg b/setup.cfg
index 56f808a63..41aef5656 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -66,9 +66,9 @@ redis =
 workers =
   kombu>=4.3.0 # BSD
 eventlet =
-  eventlet!=0.18.3,!=0.20.1,!=0.21.0,>=0.18.2 # MIT
+  eventlet>=0.18.2 # MIT
 database =
-  SQLAlchemy!=1.1.5,!=1.1.6,!=1.1.7,!=1.1.8,>=1.0.10 # MIT
+  SQLAlchemy>=1.0.10 # MIT
   alembic>=0.8.10 # MIT
   SQLAlchemy-Utils>=0.30.11 # BSD License
   PyMySQL>=0.7.6 # MIT License
diff --git a/test-requirements.txt b/test-requirements.txt
index c9c3dd0f5..69f1a9682 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -13,10 +13,10 @@ redis>=4.0.0 # MIT
 kombu>=4.3.0 # BSD
 
 # eventlet
-eventlet!=0.18.3,!=0.20.1,!=0.21.0,>=0.18.2 # MIT
+eventlet>=0.18.2 # MIT
 
 # database
-SQLAlchemy!=1.1.5,!=1.1.6,!=1.1.7,!=1.1.8,>=1.0.10 # MIT
+SQLAlchemy>=1.0.10 # MIT
 alembic>=0.8.10 # MIT
 SQLAlchemy-Utils>=0.30.11 # BSD License
 PyMySQL>=0.7.6 # MIT License