diff --git a/test/test_environment.py b/test/test_environment.py
index aa56bb44..1035a0bf 100644
--- a/test/test_environment.py
+++ b/test/test_environment.py
@@ -100,63 +100,3 @@ def test_overridden_path(tmp_path: Path, capfd: pytest.CaptureFixture[str]) -> N
     assert "python available on PATH doesn't match our installed instance" in captured.err.replace(
         "venv", "installed"
     )
-
-
-@pytest.mark.parametrize(
-    "build_frontend",
-    [
-        pytest.param("pip", marks=utils.skip_if_pyodide("No pip for pyodide")),
-        pytest.param(
-            "build",
-            marks=utils.skip_if_pyodide(
-                "pyodide doesn't support multiple values for PIP_CONSTRAINT"
-            ),
-        ),
-    ],
-)
-def test_overridden_pip_constraint(tmp_path: Path, build_frontend: str) -> None:
-    """
-    Verify that users can use PIP_CONSTRAINT to specify a specific version of
-    a build-system.requires dependency, by asserting the version of pytz in the
-    setup.py.
-    """
-    project_dir = tmp_path / "project"
-
-    project = test_projects.new_c_project(
-        setup_py_add=textwrap.dedent(
-            """
-            import pytz
-            assert pytz.__version__ == "2022.4", f"{pytz.__version__!r} != '2022.4'"
-        """
-        )
-    )
-    project.files["pyproject.toml"] = textwrap.dedent(
-        """
-        [build-system]
-        requires = ["setuptools", "pytz"]
-        build-backend = "setuptools.build_meta"
-    """
-    )
-    project.generate(project_dir)
-
-    if utils.get_platform() == "linux":
-        # put the constraints file in the project directory, so it's available
-        # in the docker container
-        constraints_file = project_dir / "constraints.txt"
-    else:
-        constraints_file = tmp_path / "constraints.txt"
-
-    constraints_file.write_text("pytz==2022.4")
-
-    actual_wheels = utils.cibuildwheel_run(
-        project_dir,
-        add_env={
-            "CIBW_BUILD_FRONTEND": build_frontend,
-            "PIP_CONSTRAINT": str(constraints_file),
-            "CIBW_ENVIRONMENT_LINUX": "PIP_CONSTRAINT=./constraints.txt",
-        },
-        single_python=True,
-    )
-
-    expected_wheels = utils.expected_wheels("spam", "0.1.0", single_python=True)
-    assert set(actual_wheels) == set(expected_wheels)