diff --git a/lower-constraints.txt b/lower-constraints.txt
index cac7563ecb..ee9acd4d94 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -25,7 +25,7 @@ fixtures==3.0.0
 future==0.16.0
 gitdb2==2.0.3
 GitPython==2.1.8
-greenlet==0.3.3
+greenlet==0.4.14
 idna==2.6
 imagesize==1.0.0
 iso8601==0.1.12
diff --git a/requirements.txt b/requirements.txt
index 6105b8e4a3..4ae431c958 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -3,7 +3,7 @@
 # process, which may cause wedges in the gate later.
 
 eventlet>=0.25.0,!=0.34.3               # MIT
-greenlet>=0.3.3
+greenlet>=0.4.14
 PasteDeploy>=2.0.0
 lxml>=4.2.3
 requests>=2.14.2                        # Apache-2.0
diff --git a/tox.ini b/tox.ini
index e0f8a352f2..b725f400e8 100644
--- a/tox.ini
+++ b/tox.ini
@@ -149,7 +149,7 @@ deps =
   -c{toxinidir}/lower-constraints.txt
   -r{toxinidir}/test-requirements.txt
   -r{toxinidir}/requirements.txt
-basepython = python3.6
+basepython = python3.7
 
 [testenv:pdf-docs]
 deps = {[testenv:docs]deps}