diff --git a/py36-constraints.txt b/py36-constraints.txt
new file mode 100644
index 0000000000..623746daa5
--- /dev/null
+++ b/py36-constraints.txt
@@ -0,0 +1,88 @@
+# taken from last passing py36 gate job prior to requirements constraining
+# oslo-log to a version that dropped py36 support, 2022-05-19
+attrs==21.4.0
+autopage==0.5.0
+bandit==1.7.1
+boto==2.49.0
+boto3==1.23.0
+botocore==1.26.0
+certifi==2022.5.18
+cffi==1.15.0
+charset-normalizer==2.0.12
+cliff==3.10.1
+cmd2==2.4.1
+coverage==6.2
+cryptography==36.0.2
+debtcollector==2.5.0
+decorator==4.4.2
+dnspython==2.2.1
+docutils==0.17.1
+dogpile.cache==1.1.5
+eventlet==0.33.1
+extras==1.0.0
+fixtures==3.0.0
+flake8==3.9.2
+future==0.18.2
+gitdb==4.0.9
+GitPython==3.1.18
+greenlet==1.1.2
+hacking==2.0.0
+idna==3.3
+importlib-metadata==4.8.3
+importlib-resources==5.4.0
+iso8601==1.0.2
+jmespath==0.10.0
+keystoneauth1==4.5.0
+keystonemiddleware==9.4.0
+lxml==4.8.0
+mccabe==0.6.1
+mock==4.0.3
+msgpack==1.0.3
+netaddr==0.8.0
+netifaces==0.11.0
+nose==1.3.7
+nosehtmloutput==0.0.7
+nosexcover==1.0.11
+os-service-types==1.7.0
+oslo.cache==2.11.0
+oslo.config==8.8.0
+oslo.context==4.1.0
+oslo.i18n==5.1.0
+oslo.log==4.7.0
+oslo.serialization==4.3.0
+oslo.utils==4.13.0
+packaging==21.3
+PasteDeploy==2.1.1
+pbr==5.9.0
+prettytable==2.5.0
+pycadf==3.1.1
+pycodestyle==2.7.0
+pycparser==2.21
+pyeclib==1.6.1
+pyflakes==2.3.1
+pyinotify==0.9.6
+pyparsing==3.0.9
+pyperclip==1.8.2
+python-dateutil==2.8.2
+python-keystoneclient==4.4.0
+python-subunit==1.4.0
+python-swiftclient==3.13.1
+pytz==2022.1
+PyYAML==6.0
+requests==2.27.1
+requests-mock==1.9.3
+rfc3986==1.5.0
+s3transfer==0.5.2
+six==1.16.0
+smmap==5.0.0
+stestr==3.2.1
+stevedore==3.5.0
+testtools==2.5.0
+typing_extensions==4.1.1
+urllib3==1.26.9
+voluptuous==0.13.1
+wcwidth==0.2.5
+WebOb==1.8.7
+wrapt==1.14.1
+xattr==0.9.9
+zipp==3.6.0
diff --git a/tools/playbooks/multinode_setup/run.yaml b/tools/playbooks/multinode_setup/run.yaml
index a186124c29..072b157cc4 100644
--- a/tools/playbooks/multinode_setup/run.yaml
+++ b/tools/playbooks/multinode_setup/run.yaml
@@ -39,4 +39,5 @@
       vars:
         tox_envlist: func-py3
         tox_environment:
+          TOX_CONSTRAINTS_FILE: https://releases.openstack.org/constraints/upper/yoga
           SWIFT_TEST_CONFIG_FILE: /home/{{ ansible_ssh_user }}/test.conf
diff --git a/tox.ini b/tox.ini
index c6acc4f53d..bcc3f373bd 100644
--- a/tox.ini
+++ b/tox.ini
@@ -29,6 +29,15 @@ deps =
   -r{toxinidir}/requirements.txt
   -r{toxinidir}/test-requirements.txt
 
+[testenv:py36]
+deps =
+  -c{toxinidir}/py36-constraints.txt
+  -r{toxinidir}/requirements.txt
+  -r{toxinidir}/test-requirements.txt
+
+[testenv:py37]
+deps = {[testenv:py36]deps}
+
 [testenv:cover]
 setenv = VIRTUAL_ENV={envdir}
          NOSE_WITH_COVERAGE=1
@@ -46,16 +55,19 @@ commands =
 
 [testenv:func-py3]
 basepython = python3
+deps = {[testenv:py36]deps}
 commands = ./.functests {posargs}
 
 [testenv:func-ec-py3]
 basepython = python3
+deps = {[testenv:py36]deps}
 commands = ./.functests {posargs}
 setenv = SWIFT_TEST_IN_PROCESS=1
          SWIFT_TEST_IN_PROCESS_CONF_LOADER=ec
 
 [testenv:func-encryption-py3]
 basepython = python3
+deps = {[testenv:py36]deps}
 commands = ./.functests {posargs}
 setenv = SWIFT_TEST_IN_PROCESS=1
          SWIFT_TEST_IN_PROCESS_CONF_LOADER=encryption