diff --git a/doc/requirements.txt b/doc/requirements.txt
index 6c8dcfb889..e34e3812bf 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,6 +1,6 @@
 openstackdocstheme>=2.2.0 # Apache-2.0
 os-api-ref>=1.4.0 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 sphinxcontrib-apidoc>=0.2.0  # BSD
 sphinxcontrib-svg2pdfconverter>=0.1.0 # BSD
diff --git a/requirements.txt b/requirements.txt
index 05eeedf599..c651a221e5 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,16 +2,13 @@
 # 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.
 
-# 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>=3.1.1 # Apache-2.0
 SQLAlchemy>=1.4.0 # MIT
 alembic>=1.4.2 # MIT
 automaton>=1.9.0 # Apache-2.0
 eventlet>=0.30.1 # MIT
 WebOb>=1.7.1 # MIT
-python-cinderclient!=4.0.0,>=3.3.0 # Apache-2.0
+python-cinderclient>=3.3.0 # Apache-2.0
 keystoneauth1>=4.2.0 # Apache-2.0
 ironic-lib>=6.0.0 # Apache-2.0
 stevedore>=1.29.0 # Apache-2.0
@@ -25,16 +22,16 @@ oslo.log>=4.3.0 # Apache-2.0
 oslo.middleware>=3.31.0 # Apache-2.0
 oslo.policy>=3.7.0 # Apache-2.0
 oslo.serialization>=2.25.0 # Apache-2.0
-oslo.service!=1.28.1,>=1.24.0 # Apache-2.0
+oslo.service>=1.24.0 # Apache-2.0
 oslo.upgradecheck>=1.3.0 # Apache-2.0
 oslo.utils>=4.5.0 # Apache-2.0
 osprofiler>=1.5.0 # Apache-2.0
 os-traits>=0.4.0 # Apache-2.0
-pecan!=1.0.2,!=1.0.3,!=1.0.4,!=1.2,>=1.0.0 # BSD
+pecan>=1.0.0 # BSD
 pycdlib>=1.11.0 # LGPLv2
 requests>=2.18.0 # Apache-2.0
 rfc3986>=1.2.0 # Apache-2.0
-jsonpatch!=1.20,>=1.16 # BSD
+jsonpatch>=1.16 # BSD
 Jinja2>=3.0.0 # BSD License (3 clause)
 keystonemiddleware>=9.5.0 # Apache-2.0
 oslo.messaging>=14.1.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 6d92131797..772496f8fe 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,8 +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.
-
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 ddt>=1.2.1 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 PyMySQL>=0.8.0 # MIT License
@@ -16,4 +12,4 @@ WebTest>=2.0.27 # MIT
 pysnmp-lextudio>=5.0.0 # BSD
 pyasn1>=0.5.1 # BSD
 pyasn1-modules>=0.3.0 # BSD
-bandit!=1.6.0,>=1.1.0,<2.0.0 # Apache-2.0
+bandit>=1.1.0,<2.0.0 # Apache-2.0