diff --git a/src/quantcore/matrix/categorical_matrix.py b/src/quantcore/matrix/categorical_matrix.py
index e95f8dd7..1f01c131 100644
--- a/src/quantcore/matrix/categorical_matrix.py
+++ b/src/quantcore/matrix/categorical_matrix.py
@@ -1,4 +1,4 @@
-from typing import List, Optional, Tuple, Union
+from typing import Any, List, Optional, Tuple, Union
 
 import numpy as np
 import pandas as pd
@@ -7,6 +7,7 @@
 from .ext.categorical import matvec, sandwich_categorical, transpose_matvec
 from .ext.split import sandwich_cat_cat, sandwich_cat_dense
 from .matrix_base import MatrixBase
+from .sparse_matrix import SparseMatrix
 from .util import (
     check_matvec_out_shape,
     check_transpose_matvec_out_shape,
@@ -15,6 +16,23 @@
 )
 
 
+def _is_indexer_full_length(full_length: int, indexer: Any):
+    if isinstance(indexer, int):
+        return full_length == 1
+    elif isinstance(indexer, list):
+        if (np.asarray(indexer) > full_length - 1).any():
+            raise IndexError("Index out-of-range.")
+        return len(set(indexer)) == full_length
+    elif isinstance(indexer, np.ndarray):
+        if (indexer > full_length - 1).any():
+            raise IndexError("Index out-of-range.")
+        return len(np.unique(indexer)) == full_length
+    elif isinstance(indexer, slice):
+        return len(range(*indexer.indices(full_length))) == full_length
+    else:
+        raise ValueError(f"Indexing with {type(indexer)} is not allowed.")
+
+
 def _none_to_slice(arr: Optional[np.ndarray], n: int) -> Union[slice, np.ndarray]:
     if arr is None or len(arr) == n:
         return slice(None, None, None)
@@ -262,8 +280,14 @@ def get_col_stds(self, weights: np.ndarray, col_means: np.ndarray) -> np.ndarray
     def __getitem__(self, item):
         if isinstance(item, tuple):
             row, col = item
-            if not (isinstance(col, slice) and col == slice(None, None, None)):
-                raise IndexError("Only column indexing is supported.")
+            if _is_indexer_full_length(self.shape[1], col):
+                if isinstance(row, int):
+                    row = [row]
+                return CategoricalMatrix(self.cat[row])
+            else:
+                # return a SparseMatrix if we subset columns
+                # TODO: this is inefficient. See issue #101.
+                return SparseMatrix(self.tocsr()[row, col], dtype=self.dtype)
         else:
             row = item
         if isinstance(row, int):
diff --git a/tests/test_categorical_matrix.py b/tests/test_categorical_matrix.py
index 876715fe..ec7e9618 100644
--- a/tests/test_categorical_matrix.py
+++ b/tests/test_categorical_matrix.py
@@ -58,3 +58,9 @@ def test_nulls(mi_element):
     vec = [0, mi_element, 1]
     with pytest.raises(ValueError, match="Categorical data can't have missing values"):
         CategoricalMatrix(vec)
+
+
+def test_categorical_indexing():
+    catvec = [0, 1, 2, 0, 1, 2]
+    mat = CategoricalMatrix(catvec)
+    mat[:, [0, 1]]