diff --git a/.zuul.yaml b/.zuul.yaml
index 77670b91393c..971c406e18dc 100644
--- a/.zuul.yaml
+++ b/.zuul.yaml
@@ -274,13 +274,6 @@
             irrelevant-files: *dsvm-irrelevant-files
         - tempest-slow-py3:
             irrelevant-files: *dsvm-irrelevant-files
-        - openstack-tox-lower-constraints:
-            # NOTE(elod.illes): with the introduction of the new dependency
-            # resolver in pip 20.3, the lower-constraints jobs start to fail
-            # as the constraint handling is now working as it should, thus
-            # revealing issues. Setting this to non-voting until the way
-            # forward is decided.
-            voting: false
         - grenade-py3:
             irrelevant-files: *dsvm-irrelevant-files
     gate:
@@ -294,13 +287,6 @@
             irrelevant-files: *dsvm-irrelevant-files
         - tempest-slow-py3:
             irrelevant-files: *dsvm-irrelevant-files
-        - openstack-tox-lower-constraints:
-            # NOTE(elod.illes): with the introduction of the new dependency
-            # resolver in pip 20.3, the lower-constraints jobs start to fail
-            # as the constraint handling is now working as it should, thus
-            # revealing issues. Setting this to non-voting until the way
-            # forward is decided.
-            voting: false
         - grenade-py3:
             irrelevant-files: *dsvm-irrelevant-files
     experimental:
diff --git a/lower-constraints.txt b/lower-constraints.txt
index 1660e2b166ba..727d578d7936 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -18,7 +18,7 @@ cmd2==0.8.1
 colorama==0.3.9
 contextlib2==0.5.5
 coverage==4.0
-cryptography==2.1
+cryptography==2.1.4
 cursive==0.2.1
 ddt==1.0.1
 debtcollector==1.19.0
@@ -53,7 +53,7 @@ kombu==4.1.0
 linecache2==1.0.0
 lxml==3.4.1
 Mako==1.0.7
-MarkupSafe==1.0
+MarkupSafe==1.1
 mccabe==0.2.1
 microversion-parse==0.2.1
 mock==2.0.0
@@ -82,7 +82,7 @@ oslo.context==2.19.2
 oslo.db==4.44.0
 oslo.i18n==3.15.3
 oslo.log==3.36.0
-oslo.messaging==6.3.0
+oslo.messaging==6.4.0
 oslo.middleware==3.31.0
 oslo.policy==1.35.0
 oslo.privsep==1.32.0
@@ -108,7 +108,7 @@ pluggy==0.6.0
 ply==3.11
 prettytable==0.7.1
 psutil==3.2.2
-psycopg2==2.6.2
+psycopg2==2.7
 py==1.5.2
 pyasn1-modules==0.2.1
 pyasn1==0.4.2
@@ -122,7 +122,7 @@ pyOpenSSL==17.5.0
 pyparsing==2.2.0
 pyperclip==1.6.0
 pypowervm==1.1.15
-pyroute2==0.4.21
+pyroute2==0.5.2
 pytest==3.4.2
 python-barbicanclient==4.5.2
 python-cinderclient==3.3.0
@@ -167,9 +167,9 @@ unittest2==1.1.0
 urllib3==1.22
 vine==1.1.4
 voluptuous==0.11.1
-warlock==1.3.0
+warlock==1.2.0
 WebOb==1.8.2
 websockify==0.8.0
 wrapt==1.10.11
 wsgi-intercept==1.7.0
-zVMCloudConnector==1.1.1
+zVMCloudConnector==1.2.2
diff --git a/requirements.txt b/requirements.txt
index aca623599e1a..83760700be54 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -10,7 +10,7 @@ Jinja2>=2.10 # BSD License (3 clause)
 keystonemiddleware>=4.17.0 # Apache-2.0
 lxml!=3.7.0,>=3.4.1 # BSD
 Routes>=2.3.1 # MIT
-cryptography>=2.1 # BSD/Apache-2.0
+cryptography>=2.1.4 # BSD/Apache-2.0
 WebOb>=1.8.2 # MIT
 # NOTE(mriedem): greenlet 0.4.14 does not work with older versions of gcc on
 # ppc64le systems, see https://github.com/python-greenlet/greenlet/issues/136.
@@ -46,7 +46,7 @@ oslo.upgradecheck>=0.1.1
 oslo.utils>=3.37.0 # Apache-2.0
 oslo.db>=4.44.0 # Apache-2.0
 oslo.rootwrap>=5.8.0 # Apache-2.0
-oslo.messaging>=6.3.0 # Apache-2.0
+oslo.messaging>=6.4.0 # Apache-2.0
 oslo.policy>=1.35.0 # Apache-2.0
 oslo.privsep>=1.32.0 # Apache-2.0
 oslo.i18n>=3.15.3 # Apache-2.0
@@ -70,5 +70,5 @@ retrying>=1.3.3,!=1.3.0 # Apache-2.0
 os-service-types>=1.2.0 # Apache-2.0
 taskflow>=2.16.0 # Apache-2.0
 python-dateutil>=2.5.3 # BSD
-zVMCloudConnector>=1.1.1;sys_platform!='win32'  # Apache 2.0 License
+zVMCloudConnector>=1.2.2;sys_platform!='win32'  # Apache 2.0 License
 futurist>=1.8.0 # Apache-2.0
diff --git a/test-requirements.txt b/test-requirements.txt
index cb1f71d2bc72..2141132b664b 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -8,7 +8,7 @@ ddt>=1.0.1 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 mock>=2.0.0 # BSD
 mox3>=0.20.0 # Apache-2.0
-psycopg2>=2.6.2 # LGPL/ZPL
+psycopg2>=2.7 # LGPL/ZPL
 PyMySQL>=0.7.6 # MIT License
 python-barbicanclient>=4.5.2 # Apache-2.0
 python-ironicclient>=2.7.0 # Apache-2.0
diff --git a/tox.ini b/tox.ini
index 5cc2dbf3acd0..a6ee0d51fbdd 100644
--- a/tox.ini
+++ b/tox.ini
@@ -283,6 +283,7 @@ commands =
   bindep test
 
 [testenv:lower-constraints]
+install_command = pip install {opts} {packages}
 deps =
   -c{toxinidir}/lower-constraints.txt
   -r{toxinidir}/test-requirements.txt