diff --git a/doc/requirements.txt b/doc/requirements.txt
index 39130db7..c9f41be1 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,8 +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
 doc8>=0.6.0 # 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 d2f44f1a..9477a18a 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,4 @@
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=2.0.0 # Apache-2.0
 alembic>=0.9.6 # MIT
 debtcollector>=1.2.0 # Apache-2.0
 oslo.i18n>=3.15.3 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index dde2d0b8..6aae3ef6 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,6 +1,6 @@
 hacking>=6.1.0,<6.2.0 # Apache-2.0
-coverage!=4.4,>=4.0 # Apache-2.0
-eventlet!=0.18.3,!=0.20.1,>=0.18.2 # MIT
+coverage>=4.0 # Apache-2.0
+eventlet>=0.18.2 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 python-subunit>=1.0.0 # Apache-2.0/BSD
 oslotest>=3.2.0 # Apache-2.0