diff --git a/packages/google-auth/google/auth/crypt/rsa.py b/packages/google-auth/google/auth/crypt/rsa.py
index 4b2fb39ffbda..639be9069549 100644
--- a/packages/google-auth/google/auth/crypt/rsa.py
+++ b/packages/google-auth/google/auth/crypt/rsa.py
@@ -24,7 +24,6 @@
 
 from google.auth import _helpers
 from google.auth.crypt import _cryptography_rsa
-from google.auth.crypt import _python_rsa
 from google.auth.crypt import base
 
 RSA_KEY_MODULE_PREFIX = "rsa.key"
@@ -37,6 +36,7 @@ class RSAVerifier(base.Verifier):
         public_key (Union["rsa.key.PublicKey", cryptography.hazmat.primitives.asymmetric.rsa.RSAPublicKey]):
             The public key used to verify signatures.
     Raises:
+        ImportError: if called with an rsa.key.PublicKey, when the rsa library is not installed
         ValueError: if an unrecognized public key is provided
     """
 
@@ -45,6 +45,8 @@ def __init__(self, public_key):
         if isinstance(public_key, RSAPublicKey):
             impl_lib = _cryptography_rsa
         elif module_str.startswith(RSA_KEY_MODULE_PREFIX):
+            from google.auth.crypt import _python_rsa
+
             impl_lib = _python_rsa
         else:
             raise ValueError(f"unrecognized public key type: {type(public_key)}")
@@ -85,6 +87,7 @@ class RSASigner(base.Signer, base.FromServiceAccountMixin):
             public key or certificate.
 
     Raises:
+        ImportError: if called with an rsa.key.PrivateKey, when the rsa library is not installed
         ValueError: if an unrecognized public key is provided
     """
 
@@ -93,6 +96,8 @@ def __init__(self, private_key, key_id=None):
         if isinstance(private_key, RSAPrivateKey):
             impl_lib = _cryptography_rsa
         elif module_str.startswith(RSA_KEY_MODULE_PREFIX):
+            from google.auth.crypt import _python_rsa
+
             impl_lib = _python_rsa
         else:
             raise ValueError(f"unrecognized private key type: {type(private_key)}")
diff --git a/packages/google-auth/noxfile.py b/packages/google-auth/noxfile.py
index 1a649812135e..e9fc880f7476 100644
--- a/packages/google-auth/noxfile.py
+++ b/packages/google-auth/noxfile.py
@@ -41,7 +41,7 @@
     "3.13",
     "3.14",
 ]
-ALL_PYTHON = UNIT_TEST_PYTHON_VERSIONS
+ALL_PYTHON = UNIT_TEST_PYTHON_VERSIONS.copy()
 ALL_PYTHON.extend(["3.7"])
 
 # Error if a python version is missing
@@ -115,16 +115,29 @@ def mypy(session):
 
 
 @nox.session(python=ALL_PYTHON)
-def unit(session):
+@nox.parametrize(["install_deprecated_extras"], (True, False))
+def unit(session, install_deprecated_extras):
     # Install all test dependencies, then install this package in-place.
 
     if session.python in ("3.7",):
         session.skip("Python 3.7 is no longer supported")
+    min_py, max_py = UNIT_TEST_PYTHON_VERSIONS[0], UNIT_TEST_PYTHON_VERSIONS[-1]
+    if not install_deprecated_extras and session.python not in (min_py, max_py):
+        # only run double tests on first and last supported versions
+        session.skip(
+            f"Extended tests only run on boundary Python versions ({min_py}, {max_py}) to reduce CI load."
+        )
 
     constraints_path = str(
         CURRENT_DIRECTORY / "testing" / f"constraints-{session.python}.txt"
     )
-    session.install("-e", ".[testing]", "-c", constraints_path)
+    extras_str = "testing"
+    if install_deprecated_extras:
+        # rsa and oauth2client were both archived and support dropped,
+        # but we still  test old code paths
+        session.install("oauth2client")
+        extras_str += ",rsa"
+    session.install("-e", f".[{extras_str}]", "-c", constraints_path)
     session.run(
         "pytest",
         f"--junitxml=unit_{session.python}_sponge_log.xml",
diff --git a/packages/google-auth/setup.py b/packages/google-auth/setup.py
index ba9e214b1cd3..8a66b7c39d0e 100644
--- a/packages/google-auth/setup.py
+++ b/packages/google-auth/setup.py
@@ -25,9 +25,6 @@
 DEPENDENCIES = (
     "pyasn1-modules>=0.2.1",
     cryptography_base_require,
-    # TODO: remove rsa from dependencies in next release (replaced with cryptography)i
-    # https://github.com/googleapis/google-auth-library-python/issues/1810
-    "rsa>=3.1.4,<5",
 )
 
 requests_extra_require = ["requests >= 2.20.0, < 3.0.0"]
@@ -46,14 +43,14 @@
 # TODO(https://github.com/googleapis/google-auth-library-python/issues/1739): Add bounds for urllib3 and packaging dependencies.
 urllib3_extra_require = ["urllib3", "packaging"]
 
+rsa_extra_require = ["rsa>=3.1.4,<5"]
+
 # Unit test requirements.
 testing_extra_require = [
     # TODO(https://github.com/googleapis/google-auth-library-python/issues/1735): Remove `grpcio` from testing requirements once an extra is added for `grpcio` dependency.
     "grpcio",
     "flask",
     "freezegun",
-    # TODO(https://github.com/googleapis/google-auth-library-python/issues/1736): Remove `oauth2client` from testing requirements once an extra is added for `oauth2client` dependency.
-    "oauth2client",
     *pyjwt_extra_require,
     "pytest",
     "pytest-cov",
@@ -86,6 +83,7 @@
     "requests": requests_extra_require,
     "testing": testing_extra_require,
     "urllib3": urllib3_extra_require,
+    "rsa": rsa_extra_require,
     # TODO(https://github.com/googleapis/google-auth-library-python/issues/1735): Add an extra for `grpcio` dependency.
     # TODO(https://github.com/googleapis/google-auth-library-python/issues/1736): Add an extra for `oauth2client` dependency.
 }
diff --git a/packages/google-auth/testing/constraints-3.8.txt b/packages/google-auth/testing/constraints-3.8.txt
index 5eba7b60e183..3ca0e8edb179 100644
--- a/packages/google-auth/testing/constraints-3.8.txt
+++ b/packages/google-auth/testing/constraints-3.8.txt
@@ -7,7 +7,6 @@
 # Then this file should have foo==1.14.0
 pyasn1-modules==0.2.1
 setuptools==40.3.0
-rsa==3.1.4
 cryptography==38.0.3
 aiohttp==3.6.2
 requests==2.20.0
diff --git a/packages/google-auth/tests/crypt/test__python_rsa.py b/packages/google-auth/tests/crypt/test__python_rsa.py
index 43539900f7fc..058c3a1abb6c 100644
--- a/packages/google-auth/tests/crypt/test__python_rsa.py
+++ b/packages/google-auth/tests/crypt/test__python_rsa.py
@@ -19,12 +19,13 @@
 
 from pyasn1_modules import pem  # type: ignore
 import pytest  # type: ignore
-import rsa  # type: ignore
 
 from google.auth import _helpers
 from google.auth.crypt import _python_rsa
 from google.auth.crypt import base
 
+rsa = pytest.importorskip("rsa")  # type: ignore
+
 
 DATA_DIR = os.path.join(os.path.dirname(__file__), "..", "data")
 
diff --git a/packages/google-auth/tests/crypt/test_rsa.py b/packages/google-auth/tests/crypt/test_rsa.py
index 6f7aa2691330..4f722a6380b0 100644
--- a/packages/google-auth/tests/crypt/test_rsa.py
+++ b/packages/google-auth/tests/crypt/test_rsa.py
@@ -18,10 +18,15 @@
 from cryptography.hazmat import backends
 from cryptography.hazmat.primitives import serialization
 import pytest
-import rsa as rsa_lib
+
+try:
+    import rsa as rsa_lib
+    from google.auth.crypt import _python_rsa
+except ImportError:
+    rsa_lib = None
+    _pyrhon_rsa = None
 
 from google.auth.crypt import _cryptography_rsa
-from google.auth.crypt import _python_rsa
 from google.auth.crypt import rsa
 
 
@@ -70,11 +75,13 @@ def test_init_with_cryptography_key(self, cryptography_public_key):
         assert isinstance(verifier._impl, _cryptography_rsa.RSAVerifier)
         assert verifier._impl._pubkey == cryptography_public_key
 
+    @pytest.mark.skipif(not rsa_lib, reason="rsa library not installed")
     def test_init_with_rsa_key(self, rsa_public_key):
         verifier = rsa.RSAVerifier(rsa_public_key)
         assert isinstance(verifier._impl, _python_rsa.RSAVerifier)
         assert verifier._impl._pubkey == rsa_public_key
 
+    @pytest.mark.skipif(not rsa_lib, reason="rsa library not installed")
     def test_warning_with_rsa(self, rsa_public_key):
         with pytest.warns(DeprecationWarning, match="The 'rsa' library is deprecated"):
             rsa.RSAVerifier(rsa_public_key)
@@ -114,12 +121,14 @@ def test_init_with_cryptography_key(self, cryptography_private_key):
         assert signer._impl._key == cryptography_private_key
         assert signer._impl.key_id == "123"
 
+    @pytest.mark.skipif(not rsa_lib, reason="rsa library not installed")
     def test_init_with_rsa_key(self, rsa_private_key):
         signer = rsa.RSASigner(rsa_private_key, key_id="123")
         assert isinstance(signer._impl, _python_rsa.RSASigner)
         assert signer._impl._key == rsa_private_key
         assert signer._impl.key_id == "123"
 
+    @pytest.mark.skipif(not rsa_lib, reason="rsa library not installed")
     def test_warning_with_rsa(self, rsa_private_key):
         with pytest.warns(DeprecationWarning, match="The 'rsa' library is deprecated"):
             rsa.RSASigner(rsa_private_key, key_id="123")
@@ -130,8 +139,8 @@ def test_init_with_unknown_key(self):
         with pytest.raises(ValueError):
             rsa.RSASigner(unknown_key)
 
-    def test_sign_delegates(self, rsa_private_key):
-        signer = rsa.RSASigner(rsa_private_key)
+    def test_sign_delegates(self, cryptography_private_key):
+        signer = rsa.RSASigner(cryptography_private_key)
 
         with mock.patch.object(
             signer._impl, "sign", return_value=b"signature"
@@ -164,6 +173,7 @@ def test_end_to_end_cryptography_lib(self, private_key_bytes, public_key_bytes):
         assert isinstance(verifier._impl, _cryptography_rsa.RSAVerifier)
         assert isinstance(signer._impl, _cryptography_rsa.RSASigner)
 
+    @pytest.mark.skipif(not rsa_lib, reason="rsa library not installed")
     def test_end_to_end_rsa_lib(self, rsa_private_key, rsa_public_key):
         signer = rsa.RSASigner(rsa_private_key)
         message = b"Hello World"