diff --git a/test-requirements.txt b/test-requirements.txt
index d39ca54c..03dcaedd 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -9,11 +9,12 @@ oslotest>=1.10.0 # Apache-2.0
 
 # These are needed for docs generation/testing
 openstackdocstheme>=1.16.0 # Apache-2.0
-sphinx>=1.6.2 # BSD
+sphinx>=1.6.2,!=1.6.6,<2.0.0;python_version=='2.7'  # BSD
+sphinx>=1.6.2,!=1.6.6;python_version>='3.4'  # BSD
 doc8 # Apache-2.0
 reno!=2.3.1,>=1.8.0 # Apache-2.0
 
 coverage!=4.4,>=4.0 # Apache-2.0
 
 # Bandit security code scanner
-bandit>=1.1.0 # Apache-2.0
+bandit>=1.1.0,<=1.6.2 # Apache-2.0