diff --git a/build-support/known_py3_failures.txt b/build-support/known_py3_failures.txt
index 5ed53849874..a8b4d2bdb2a 100644
--- a/build-support/known_py3_failures.txt
+++ b/build-support/known_py3_failures.txt
@@ -5,7 +5,6 @@ tests/python/pants_test/backend/jvm/tasks:jar_publish
 tests/python/pants_test/backend/jvm/tasks:junit_run
 tests/python/pants_test/backend/jvm/tasks:resources_task
 tests/python/pants_test/backend/python/tasks:tasks
-tests/python/pants_test/backend/python:pants_requirement
 tests/python/pants_test/binaries:binaries
 tests/python/pants_test/build_graph:build_file_parser
 tests/python/pants_test/build_graph:build_graph
diff --git a/src/python/pants/backend/python/pants_requirement.py b/src/python/pants/backend/python/pants_requirement.py
index e60311c8b20..f1d471c7426 100644
--- a/src/python/pants/backend/python/pants_requirement.py
+++ b/src/python/pants/backend/python/pants_requirement.py
@@ -50,9 +50,7 @@ def __call__(self, name=None, dist=None):
                                       msg='The {} target only works for pantsbuild.pants '
                                           'distributions, given {}'.format(self.alias, dist))
 
-    # TODO(John Sirois): Modify to constraint to >=3.5,<4 as part of
-    # https://github.com/pantsbuild/pants/issues/6062
-    env_marker = "python_version>='2.7' and python_version<'3'"
+    env_marker = "python_version>='3.4' or (python_version>='2.7' and python_version<'3')"
 
     requirement = PythonRequirement(requirement="{key}=={version} ; {env_marker}"
                                     .format(key=dist,
diff --git a/tests/python/pants_test/backend/python/test_pants_requirement.py b/tests/python/pants_test/backend/python/test_pants_requirement.py
index ef73ef97337..7c2ef55fe88 100644
--- a/tests/python/pants_test/backend/python/test_pants_requirement.py
+++ b/tests/python/pants_test/backend/python/test_pants_requirement.py
@@ -35,9 +35,14 @@ def key(python_requirement):
     self.assertIsNotNone(req.requirement.marker)
     self.assertTrue(req.requirement.marker.evaluate(),
                     'pants_requirement() should always work in the current test environment')
-    self.assertFalse(req.requirement.marker.evaluate({'python_version': '3.5'}))
-    self.assertFalse(req.requirement.marker.evaluate({'python_version': '2.6'}))
-    self.assertTrue(req.requirement.marker.evaluate({'python_version': '2.7'}))
+
+    def evaluate_version(version):
+      return req.requirement.marker.evaluate({'python_version': version})
+
+    allowed_versions = {'2.7', '3.4', '3.5', '3.6', '3.7'}
+
+    self.assertFalse(evaluate_version('2.6'))
+    self.assertTrue(all(evaluate_version(v) for v in allowed_versions))
 
   def test_default_name(self):
     self.add_to_build_file('3rdparty/python/pants', 'pants_requirement()')