diff --git a/google/cloud/_http.py b/google/cloud/_http.py
index 8062622..fbc228e 100644
--- a/google/cloud/_http.py
+++ b/google/cloud/_http.py
@@ -15,11 +15,14 @@
 """Shared implementation of connections to API servers."""
 
 import collections
+try:
+    import collections.abc as collections_abc
+except ImportError:
+    import collections as collections_abc
 import json
 import platform
 import warnings
 
-from six.moves import collections_abc
 from six.moves.urllib.parse import urlencode
 
 from google.api_core.client_info import ClientInfo
diff --git a/noxfile.py b/noxfile.py
index 0a415ac..f663bf1 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -20,6 +20,7 @@
 
 
 DEFAULT_PYTHON_VERSION = "3.7"
+CURRENT_DIRECTORY = os.path.abspath(os.path.dirname(__file__))
 
 
 def default(session):
@@ -29,10 +30,22 @@ def default(session):
     Python corresponding to the ``nox`` binary the ``PATH`` can
     run the tests.
     """
+    constraints_path = os.path.join(
+        CURRENT_DIRECTORY,
+        "testing",
+        "constraints-{}.txt".format(session.python)
+    )
 
     # Install all test dependencies, then install local packages in-place.
-    session.install("mock", "pytest", "pytest-cov", "grpcio >= 1.0.2")
-    session.install("-e", ".")
+    session.install(
+        "mock",
+        "pytest",
+        "pytest-cov",
+        "grpcio >= 1.0.2",
+        "-c",
+        constraints_path
+    )
+    session.install("-e", ".", "-c", constraints_path)
 
     # Run py.test against the unit tests.
     session.run(
diff --git a/setup.py b/setup.py
index 8db7c0f..b816383 100644
--- a/setup.py
+++ b/setup.py
@@ -27,7 +27,12 @@
 # 'Development Status :: 4 - Beta'
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 5 - Production/Stable"
-dependencies = ["google-api-core >= 1.19.0, < 2.0.0dev"]
+dependencies = [
+    "google-api-core >= 1.21.0, < 2.0.0dev",
+    # Support six==1.12.0 due to App Engine standard runtime.
+    # https://github.com/googleapis/python-cloud-core/issues/45
+    "six >=1.12.0",
+]
 extras = {"grpc": "grpcio >= 1.8.2, < 2.0dev"}
 
 
diff --git a/testing/constraints-2.7.txt b/testing/constraints-2.7.txt
new file mode 100644
index 0000000..8679811
--- /dev/null
+++ b/testing/constraints-2.7.txt
@@ -0,0 +1,2 @@
+google-api-core==1.21.0
+six==1.12.0
diff --git a/testing/constraints-3.5.txt b/testing/constraints-3.5.txt
new file mode 100644
index 0000000..8679811
--- /dev/null
+++ b/testing/constraints-3.5.txt
@@ -0,0 +1,2 @@
+google-api-core==1.21.0
+six==1.12.0
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
new file mode 100644
index 0000000..e69de29
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
new file mode 100644
index 0000000..e69de29
diff --git a/testing/constraints-3.8.txt b/testing/constraints-3.8.txt
new file mode 100644
index 0000000..e69de29