diff --git a/doc/requirements.txt b/doc/requirements.txt
index 8c84b1e4..3ab2f2b8 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.
 # this is required for the docs build jobs
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.0.0 # BSD
 openstackdocstheme>=2.2.0 # Apache-2.0
 reno>=3.1.0 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
diff --git a/test-requirements.txt b/test-requirements.txt
index 2a80df18..4af9398a 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,4 +1,4 @@
-eventlet>=0.18.2,!=0.18.3,!=0.20.1,!=0.21.0,!=0.23.0 # MIT
+eventlet>=0.18.2 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 testscenarios>=0.4 # Apache-2.0/BSD
 testtools>=2.2.0 # MIT
@@ -6,10 +6,7 @@ oslotest>=3.2.0 # Apache-2.0
 ddt>=1.0.1 # MIT
 stestr>=2.0.0 # Apache-2.0
 
-# when we can require tox>= 1.4, this can go into tox.ini:
-#  [testenv:cover]
-#  deps = {[testenv]deps} coverage
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.0 # Apache-2.0
 
 # used for oslotest cross-testing scripts
 oslo.config>=5.2.0 # Apache-2.0