diff --git a/noxfile.py b/noxfile.py
index 89c6668ba3..767def3795 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -104,9 +104,11 @@ def unit(session, oauth2client):
     session.install("setuptools", "wheel")
     session.run("python3", "setup.py", "bdist_wheel")
     session.install(os.path.join("dist", os.listdir("dist").pop()))
+    root_dir = os.path.dirname(os.path.realpath(__file__))
+    constraints_path = str(f"{root_dir}/testing/constraints-{session.python}.txt")
+    session.install("-r", constraints_path)
 
     # Run tests from a different directory to test the package artifacts
-    root_dir = os.path.dirname(os.path.realpath(__file__))
     temp_dir = session.create_tmp()
     session.chdir(temp_dir)
     shutil.copytree(os.path.join(root_dir, "tests"), "tests")
diff --git a/setup.py b/setup.py
index 105cb1c4a8..6f735a2fc4 100644
--- a/setup.py
+++ b/setup.py
@@ -33,12 +33,12 @@
 packages = ["apiclient", "googleapiclient", "googleapiclient/discovery_cache"]
 
 install_requires = [
-    "httplib2>=0.15.0,<1.dev0",
+    "httplib2>=0.19.0,<1.dev0",
     # NOTE: Maintainers, please do not require google-auth>=2.x.x
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
-    "google-auth>=1.19.0,<3.0.0.dev0",
-    "google-auth-httplib2>=0.1.0",
+    "google-auth>=1.32.0,<3.0.0.dev0,!=2.24.0,!=2.25.0",
+    "google-auth-httplib2>=0.2.0, <1.0.0",
     # NOTE: Maintainers, please do not require google-api-core>=2.x.x
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
diff --git a/testing/constraints-3.10.txt b/testing/constraints-3.10.txt
index e69de29bb2..e474f9c699 100644
--- a/testing/constraints-3.10.txt
+++ b/testing/constraints-3.10.txt
@@ -0,0 +1,6 @@
+# Test an old version of google-auth against the latest version of api-core.
+httplib2==0.19.0
+google-auth==1.32.0
+google-auth-httplib2==0.2.0
+google-api-core
+uritemplate==3.0.1
\ No newline at end of file
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index 55f99b726f..63319d20e0 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -5,8 +5,9 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-httplib2==0.15.0
-google-auth==1.19.0
-google-auth-httplib2==0.0.3
+# Test minimum requirements.
+httplib2==0.19.0
+google-auth==1.32.0
+google-auth-httplib2==0.2.0
 google-api-core==1.31.5
 uritemplate==3.0.1
\ No newline at end of file
diff --git a/testing/constraints-3.8.txt b/testing/constraints-3.8.txt
index e69de29bb2..72dd399a25 100644
--- a/testing/constraints-3.8.txt
+++ b/testing/constraints-3.8.txt
@@ -0,0 +1,6 @@
+# Test a new version of google-auth against the minimum supported version of api-core.
+httplib2==0.19.0
+google-auth
+google-auth-httplib2==0.2.0
+google-api-core==1.31.5
+uritemplate==3.0.1
\ No newline at end of file
diff --git a/testing/constraints-3.9.txt b/testing/constraints-3.9.txt
index e69de29bb2..f12503bc12 100644
--- a/testing/constraints-3.9.txt
+++ b/testing/constraints-3.9.txt
@@ -0,0 +1,7 @@
+# Test the latest version of google-auth against the version of
+# api-core with ClientOptions.universe_domain.
+httplib2==0.19.0
+google-auth
+google-auth-httplib2==0.2.0
+google-api-core==2.15.0
+uritemplate==3.0.1
\ No newline at end of file