diff --git a/doc/requirements.txt b/doc/requirements.txt
index df112fe733f0..2a795807a485 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -1,7 +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.
-sphinx>=2.0.0,!=2.1.0 # BSD
+sphinx>=2.1.1 # BSD
 sphinxcontrib-actdiag>=0.8.5 # BSD
 sphinxcontrib-seqdiag>=0.8.4 # BSD
 sphinxcontrib-svg2pdfconverter>=0.1.0 # BSD
diff --git a/requirements.txt b/requirements.txt
index 93c845533ce1..eb158af1c067 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -22,7 +22,7 @@ netifaces>=0.10.4 # MIT
 paramiko>=2.7.1 # LGPLv2.1+
 iso8601>=0.1.11 # MIT
 jsonschema>=4.0.0 # MIT
-python-cinderclient!=4.0.0,>=3.3.0 # Apache-2.0
+python-cinderclient>=4.0.1 # Apache-2.0
 keystoneauth1>=3.16.0 # Apache-2.0
 python-neutronclient>=7.1.0 # Apache-2.0
 python-glanceclient>=2.8.0 # Apache-2.0
@@ -58,7 +58,7 @@ castellan>=0.16.0 # Apache-2.0
 microversion-parse>=0.2.1 # Apache-2.0
 tooz>=1.58.0 # Apache-2.0
 cursive>=0.2.1 # Apache-2.0
-retrying>=1.3.3,!=1.3.0 # Apache-2.0
+retrying>=1.3.3 # Apache-2.0
 os-service-types>=1.7.0 # Apache-2.0
 python-dateutil>=2.7.0 # BSD
 futurist>=1.8.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 04dcc056ee53..ae5d8c8a45c9 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,5 +1,5 @@
 hacking==6.1.0 # Apache-2.0
-coverage!=4.4,>=4.0 # Apache-2.0
+coverage>=4.4.1 # Apache-2.0
 ddt>=1.2.1 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 psycopg2-binary>=2.8 # LGPL/ZPL