diff --git a/doc/requirements.txt b/doc/requirements.txt
index a31064447..1cb533636 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
 sphinx-feature-classification>=0.2.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index 157d76169..562eb161b 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
+coverage>=4.4.1 # Apache-2.0
 fixtures>=3.0.0 # Apache-2.0/BSD
 # NOTE(tetsuro): Local testing on osx may have problems to install packages,
 # psycopg2 and PYMySQL. You can workaround them using sys_platform qualifier.