diff --git a/doc/requirements.txt b/doc/requirements.txt
index 5b783654..53f142ec 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -4,7 +4,8 @@
 
 # For generating sphinx documentation
 openstackdocstheme>=1.18.1 # Apache-2.0
-sphinx!=1.6.6,!=1.6.7,>=1.6.2 # BSD
+sphinx!=1.6.6,!=1.6.7,>=1.6.2,<2.0.0;python_version=='2.7' # BSD
+sphinx!=1.6.6,!=1.6.7,>=1.6.2;python_version>='3.4' # BSD
 reno>=2.5.0 # Apache-2.0
 sphinxcontrib-apidoc>=0.2.0  # BSD
 
diff --git a/test-requirements.txt b/test-requirements.txt
index 4a287355..98c68238 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -6,7 +6,7 @@ mock>=2.0.0 # BSD
 oslotest>=3.2.0 # Apache-2.0
 pifpaf>=0.10.0 # Apache-2.0
 # Bandit security code scanner
-bandit>=1.1.0 # Apache-2.0
+bandit>=1.1.0,<1.6.0 # Apache-2.0
 stestr>=2.0.0 # Apache-2.0
 python-memcached>=1.56 # PSF
 pymongo!=3.1,>=3.0.2 # Apache-2.0