diff --git a/packages/google-cloud-container/.pre-commit-config.yaml b/packages/google-cloud-container/.pre-commit-config.yaml
index a9024b15d725..32302e4883a1 100644
--- a/packages/google-cloud-container/.pre-commit-config.yaml
+++ b/packages/google-cloud-container/.pre-commit-config.yaml
@@ -12,6 +12,6 @@ repos:
     hooks:
     - id: black
 -   repo: https://gitlab.com/pycqa/flake8
-    rev: 3.8.4
+    rev: 3.9.0
     hooks:
     - id: flake8
diff --git a/packages/google-cloud-container/noxfile.py b/packages/google-cloud-container/noxfile.py
index 9fafb0c28f60..2efbe2b5ff38 100644
--- a/packages/google-cloud-container/noxfile.py
+++ b/packages/google-cloud-container/noxfile.py
@@ -18,6 +18,7 @@
 
 from __future__ import absolute_import
 import os
+import pathlib
 import shutil
 
 import nox
@@ -30,6 +31,8 @@
 SYSTEM_TEST_PYTHON_VERSIONS = ["3.8"]
 UNIT_TEST_PYTHON_VERSIONS = ["3.6", "3.7", "3.8", "3.9"]
 
+CURRENT_DIRECTORY = pathlib.Path(__file__).parent.absolute()
+
 # 'docfx' is excluded since it only needs to run in 'docs-presubmit'
 nox.options.sessions = [
     "unit",
@@ -84,13 +87,15 @@ def lint_setup_py(session):
 
 def default(session):
     # Install all test dependencies, then install this package in-place.
-    session.install("asyncmock", "pytest-asyncio")
 
-    session.install(
-        "mock", "pytest", "pytest-cov",
+    constraints_path = str(
+        CURRENT_DIRECTORY / "testing" / f"constraints-{session.python}.txt"
     )
+    session.install("asyncmock", "pytest-asyncio", "-c", constraints_path)
 
-    session.install("-e", ".")
+    session.install("mock", "pytest", "pytest-cov", "-c", constraints_path)
+
+    session.install("-e", ".", "-c", constraints_path)
 
     # Run py.test against the unit tests.
     session.run(
@@ -117,6 +122,9 @@ def unit(session):
 @nox.session(python=SYSTEM_TEST_PYTHON_VERSIONS)
 def system(session):
     """Run the system test suite."""
+    constraints_path = str(
+        CURRENT_DIRECTORY / "testing" / f"constraints-{session.python}.txt"
+    )
     system_test_path = os.path.join("tests", "system.py")
     system_test_folder_path = os.path.join("tests", "system")
 
@@ -141,10 +149,8 @@ def system(session):
 
     # Install all test dependencies, then install this package into the
     # virtualenv's dist-packages.
-    session.install(
-        "mock", "pytest", "google-cloud-testutils",
-    )
-    session.install("-e", ".")
+    session.install("mock", "pytest", "google-cloud-testutils", "-c", constraints_path)
+    session.install("-e", ".", "-c", constraints_path)
 
     # Run py.test against the system tests.
     if system_test_exists:
diff --git a/packages/google-cloud-container/synth.metadata b/packages/google-cloud-container/synth.metadata
index 8b5c788a6855..3082d2db019d 100644
--- a/packages/google-cloud-container/synth.metadata
+++ b/packages/google-cloud-container/synth.metadata
@@ -19,7 +19,7 @@
       "git": {
         "name": "synthtool",
         "remote": "https://github.com/googleapis/synthtool.git",
-        "sha": "79c8dd7ee768292f933012d3a69a5b4676404cda"
+        "sha": "86ed43d4f56e6404d068e62e497029018879c771"
       }
     }
   ],
diff --git a/packages/google-cloud-container/testing/constraints-3.6.txt b/packages/google-cloud-container/testing/constraints-3.6.txt
index af597f7a6501..399fa9e88e71 100644
--- a/packages/google-cloud-container/testing/constraints-3.6.txt
+++ b/packages/google-cloud-container/testing/constraints-3.6.txt
@@ -5,7 +5,7 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-google-api-core==1.21.2
+google-api-core==1.26.3
 grpc-google-iam-v1==0.12.3
 proto-plus==1.4.0
 libcst==0.2.5
\ No newline at end of file