diff --git a/noxfile.py b/noxfile.py
index a6201b664f..2f1b0f1b98 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -76,7 +76,7 @@ def default(session):
     # Install all test dependencies, then install this package in-place.
     session.install("asyncmock", "pytest-asyncio")
 
-    session.install("mock", "pytest", "pytest-cov")
+    session.install("mock", "pytest", "pytest-cov", "pytz")
     session.install("-e", ".")
 
     # Run py.test against the unit tests.
@@ -150,6 +150,7 @@ def system(session):
         "mock",
         "pytest",
         "google-cloud-testutils",
+        "pytz",
     )
     session.install("-e", ".[tracing]")
 
diff --git a/setup.py b/setup.py
index 87f3e26874..c20a714925 100644
--- a/setup.py
+++ b/setup.py
@@ -29,8 +29,8 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
-    "google-api-core[grpc] >= 1.22.0, < 2.0.0dev",
-    "google-cloud-core >= 1.4.1, < 2.0dev",
+    "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
+    "google-cloud-core >= 1.4.1, < 3.0dev",
     "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
     "libcst >= 0.2.5",
     "proto-plus == 1.11.0",