diff --git a/doc/requirements.txt b/doc/requirements.txt
index 5f0bf6a..99f7e90 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,3 +1,3 @@
-sphinx!=1.6.6,!=1.6.7,>=1.6.2 # BSD
+sphinx>=1.7.0 # BSD
 openstackdocstheme>=1.31.2 # Apache-2.0
 reno>=2.5.0 # Apache-2.0
diff --git a/requirements.txt b/requirements.txt
index 108bbee..ae5ea16 100644
--- a/requirements.txt
+++ b/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.
-
-pbr!=2.1.0,>=2.0.0 # Apache-2.0
+pbr>=3.0.0 # Apache-2.0
 
 ddt>=1.6.0 # MIT
 oslo.log>=3.36.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index e422e93..761bf70 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.
+hacking>=3.0.1,<3.1.0 # Apache-2.0
 
-hacking>=3.0.1,<3.1.0;python_version>'3' # Apache-2.0
-
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 python-subunit>=1.0.0 # Apache-2.0/BSD
 oslotest>=3.2.0 # Apache-2.0
 stestr>=1.0.0 # Apache-2.0