diff --git a/noxfile.py b/noxfile.py
index e74321f49..804225c8c 100644
--- a/noxfile.py
+++ b/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",
@@ -78,13 +81,14 @@ 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(
@@ -136,6 +140,10 @@ def system_emulated(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")
 
@@ -147,7 +155,7 @@ def system(session):
         session.skip("Credentials must be set via environment variable")
     # Install pyopenssl for mTLS testing.
     if os.environ.get("GOOGLE_API_USE_CLIENT_CERTIFICATE", "false") == "true":
-        session.install("pyopenssl")
+        session.install("pyopenssl", "-c", constraints_path)
 
     system_test_exists = os.path.exists(system_test_path)
     system_test_folder_exists = os.path.exists(system_test_folder_path)
@@ -160,10 +168,8 @@ 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/setup.py b/setup.py
index 21a0126f3..2a4362deb 100644
--- a/setup.py
+++ b/setup.py
@@ -29,7 +29,7 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
-    "google-api-core[grpc] >= 1.22.2, < 2.0.0dev",
+    "google-api-core[grpc] >= 1.26.0, < 2.0.0dev",
     "google-cloud-core >= 1.4.1, < 2.0dev",
     "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
     "proto-plus >= 1.13.0",
diff --git a/testing/constraints-3.10.txt b/testing/constraints-3.10.txt
new file mode 100644
index 000000000..e69de29bb
diff --git a/testing/constraints-3.6.txt b/testing/constraints-3.6.txt
new file mode 100644
index 000000000..25d8d3eef
--- /dev/null
+++ b/testing/constraints-3.6.txt
@@ -0,0 +1,14 @@
+# This constraints file is used to check that lower bounds
+# are correct in setup.py
+# List *all* library dependencies and extras in this file.
+# Pin the version to the lower bound.
+#
+# 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==1.26.0
+google-cloud-core==1.4.1
+grpc-google-iam-v1==0.12.3
+proto-plus==1.13.0
+libcst==0.2.5
+packaging==14.3
+google-auth==1.24.0  # TODO: remove when google-auth >= 1.25.0 is required transitively through google-api-core
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
new file mode 100644
index 000000000..e69de29bb
diff --git a/testing/constraints-3.8.txt b/testing/constraints-3.8.txt
new file mode 100644
index 000000000..e69de29bb
diff --git a/testing/constraints-3.9.txt b/testing/constraints-3.9.txt
new file mode 100644
index 000000000..e69de29bb