diff --git a/doc/requirements.txt b/doc/requirements.txt
index 244b6b6c..dc949b25 100644
--- a/doc/requirements.txt
+++ b/doc/requirements.txt
@@ -2,6 +2,7 @@
 # of appearance. Changing the order has an impact on the overall integration
 # process, which may cause wedges in the gate later.
 
-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
 openstackdocstheme>=1.18.1 # Apache-2.0
 reno>=2.5.0 # Apache-2.0
diff --git a/lower-constraints.txt b/lower-constraints.txt
index c6cbe344..68970847 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -23,7 +23,7 @@ linecache2==1.0.0
 MarkupSafe==1.0
 mccabe==0.2.1
 mock==2.0.0
-monotonic==1.4
+monotonic==1.4;python_version<'3.3'
 mox3==0.25.0
 msgpack==0.5.6
 netaddr==0.7.19
diff --git a/requirements.txt b/requirements.txt
index 303bce23..a25e739f 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -12,4 +12,4 @@ oslo.serialization>=2.25.0 # Apache-2.0
 debtcollector>=1.19.0 # Apache-2.0
 pyinotify>=0.9.6;sys_platform!='win32' and sys_platform!='darwin' and sys_platform!='sunos5' # MIT
 python-dateutil>=2.7.0 # BSD
-monotonic>=1.4 # Apache-2.0
+monotonic>=1.4;python_version<'3.3' # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index ad8d09a1..e119f198 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -15,4 +15,4 @@ oslotest>=3.3.0 # Apache-2.0
 coverage>=4.5.1 # Apache-2.0
 
 # Bandit security code scanner
-bandit>=1.1.0 # Apache-2.0
+bandit>=1.1.0,<1.6.0 # Apache-2.0