diff --git a/doc/requirements.txt b/doc/requirements.txt
index 60abdfd59..353e57efd 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,6 +1,6 @@
 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-svg2pdfconverter>=0.1.0 # BSD
 sphinxcontrib-apidoc>=0.2.0  # BSD
 openstackdocstheme>=2.2.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index 7951400da..53f122140 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,9 +2,6 @@
 # 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.
 automaton>=1.9.0 # Apache-2.0
 alembic>=1.4.2 # MIT
 construct>=2.9.39 # MIT
diff --git a/test-requirements.txt b/test-requirements.txt
index 99c5fd381..84a6235fc 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.
-
-bandit!=1.6.0,>=1.1.0,<2.0.0 # Apache-2.0
-coverage!=4.4,>=4.0 # Apache-2.0
-pymemcache!=1.3.0,>=1.2.9 # Apache-2.0
+bandit>=1.1.0,<2.0.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
+pymemcache>=1.2.9 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 oslotest>=3.2.0 # Apache-2.0