diff --git a/pyproject.toml b/pyproject.toml
index 2d387a6..65693d7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -63,3 +63,11 @@ known-third-party = []
 
 [tool.ruff.lint.flake8-tidy-imports]
 ban-relative-imports = "all"
+
+[tool.coverage.run]
+source = ["xarray_array_testing"]
+branch = true
+
+[tool.coverage.report]
+show_missing = true
+exclude_lines = ["pragma: no cover", "if TYPE_CHECKING"]
diff --git a/xarray_array_testing/indexing.py b/xarray_array_testing/indexing.py
new file mode 100644
index 0000000..d7d1a02
--- /dev/null
+++ b/xarray_array_testing/indexing.py
@@ -0,0 +1,80 @@
+from contextlib import nullcontext
+
+import hypothesis.extra.numpy as npst
+import hypothesis.strategies as st
+import xarray.testing.strategies as xrst
+from hypothesis import given
+
+from xarray_array_testing.base import DuckArrayTestMixin
+
+
+def scalar_indexer(size):
+    return st.integers(min_value=-size, max_value=size - 1)
+
+
+def integer_array_indexer(size):
+    dtypes = npst.integer_dtypes()
+
+    return npst.arrays(
+        dtypes, size, elements={"min_value": -size, "max_value": size - 1}
+    )
+
+
+def indexers(size, indexer_types):
+    indexer_strategy_fns = {
+        "scalars": scalar_indexer,
+        "slices": st.slices,
+        "integer_arrays": integer_array_indexer,
+    }
+
+    bad_types = set(indexer_types) - indexer_strategy_fns.keys()
+    if bad_types:
+        raise ValueError(f"unknown indexer strategies: {sorted(bad_types)}")
+
+    # use the order of definition to prefer simpler strategies over more complex
+    # ones
+    indexer_strategies = [
+        strategy_fn(size)
+        for name, strategy_fn in indexer_strategy_fns.items()
+        if name in indexer_types
+    ]
+    return st.one_of(*indexer_strategies)
+
+
+@st.composite
+def orthogonal_indexers(draw, sizes, indexer_types):
+    # TODO: make use of `flatmap` and `builds` instead of `composite`
+    possible_indexers = {
+        dim: indexers(size, indexer_types) for dim, size in sizes.items()
+    }
+    concrete_indexers = draw(xrst.unique_subset_of(possible_indexers))
+    return {dim: draw(indexer) for dim, indexer in concrete_indexers.items()}
+
+
+class IndexingTests(DuckArrayTestMixin):
+    @property
+    def orthogonal_indexer_types(self):
+        return st.sampled_from(["scalars", "slices"])
+
+    @staticmethod
+    def expected_errors(op, **parameters):
+        return nullcontext()
+
+    @given(st.data())
+    def test_variable_isel_orthogonal(self, data):
+        indexer_types = data.draw(
+            st.lists(self.orthogonal_indexer_types, min_size=1, unique=True)
+        )
+        variable = data.draw(xrst.variables(array_strategy_fn=self.array_strategy_fn))
+        idx = data.draw(orthogonal_indexers(variable.sizes, indexer_types))
+
+        with self.expected_errors(
+            "isel_orthogonal", variable=variable, indexer_types=indexer_types
+        ):
+            actual = variable.isel(idx).data
+
+            raw_indexers = {dim: idx.get(dim, slice(None)) for dim in variable.dims}
+            expected = variable.data[*raw_indexers.values()]
+
+        assert isinstance(actual, self.array_type), f"wrong type: {type(actual)}"
+        self.assert_equal(actual, expected)
diff --git a/xarray_array_testing/tests/test_numpy.py b/xarray_array_testing/tests/test_numpy.py
index 2a9d95b..648f69d 100644
--- a/xarray_array_testing/tests/test_numpy.py
+++ b/xarray_array_testing/tests/test_numpy.py
@@ -5,6 +5,7 @@
 
 from xarray_array_testing.base import DuckArrayTestMixin
 from xarray_array_testing.creation import CreationTests
+from xarray_array_testing.indexing import IndexingTests
 from xarray_array_testing.reduction import ReductionTests
 
 
@@ -32,3 +33,7 @@ class TestCreationNumpy(CreationTests, NumpyTestMixin):
 
 class TestReductionNumpy(ReductionTests, NumpyTestMixin):
     pass
+
+
+class TestIndexingNumpy(IndexingTests, NumpyTestMixin):
+    pass