diff --git a/pretab/transformers/splines/base_spline.py b/pretab/transformers/splines/base_spline.py
index 256de14..104a268 100644
--- a/pretab/transformers/splines/base_spline.py
+++ b/pretab/transformers/splines/base_spline.py
@@ -123,7 +123,7 @@ class BaseSplineTransformer(BasePreTabTransformer):
     >>> from pretab.transformers import BSplineTransformer
     >>> X = np.linspace(0, 1, 50).reshape(-1, 1)
     >>> BSplineTransformer(output_dim=8).fit_transform(X).shape
-    (50, 9)
+    (50, 8)
     """
 
     def __init__(
diff --git a/pretab/transformers/splines/bspline.py b/pretab/transformers/splines/bspline.py
index 72838a7..0adcf90 100644
--- a/pretab/transformers/splines/bspline.py
+++ b/pretab/transformers/splines/bspline.py
@@ -24,7 +24,15 @@ class BSplineTransformer(BaseSplineTransformer):
     is expanded column by column and the results are stacked horizontally.
 
     See :class:`~pretab.transformers.splines.base_spline.BaseSplineTransformer`
-    for the full parameter description. ``include_bias`` defaults to True here.
+    for the full parameter description.
+
+    .. note::
+       ``include_bias`` defaults to ``False``. A B-spline basis over a clamped
+       knot vector is a partition of unity -- every row sums to 1 -- so an
+       extra intercept column is an exact linear combination of the basis and
+       makes the design matrix singular. Set it to ``True`` only if a
+       downstream model needs the explicit column and tolerates the
+       collinearity.
 
     Examples
     --------
@@ -32,14 +40,14 @@ class BSplineTransformer(BaseSplineTransformer):
     >>> from pretab.transformers import BSplineTransformer
     >>> X = np.linspace(0, 1, 50).reshape(-1, 1)
     >>> BSplineTransformer(output_dim=8).fit_transform(X).shape
-    (50, 9)
+    (50, 8)
     """
 
     def __init__(
         self,
         output_dim=UNSET,
         degree: int = 3,
-        include_bias: bool = True,
+        include_bias: bool = False,
         knot_locations: np.ndarray | None = None,
         target_aware: bool = False,
         placement_strategy: str = "quantile",
diff --git a/tests/test_adaptive_output_dim.py b/tests/test_adaptive_output_dim.py
index 745beb0..a70fa47 100644
--- a/tests/test_adaptive_output_dim.py
+++ b/tests/test_adaptive_output_dim.py
@@ -56,8 +56,7 @@
     "tprs": OUTPUT_DIM,
     "mspline": OUTPUT_DIM,
     "ispline": OUTPUT_DIM,
-    # B-spline defaults to include_bias=True -> output_dim + 1
-    "bspline": OUTPUT_DIM + 1,
+    "bspline": OUTPUT_DIM,
 }
 
 # Families that honor the adaptive window when driven through the Preprocessor.
diff --git a/tests/test_spline_expansions.py b/tests/test_spline_expansions.py
index 40e50e2..e350208 100644
--- a/tests/test_spline_expansions.py
+++ b/tests/test_spline_expansions.py
@@ -132,3 +132,46 @@ def test_spline_penalty_matrix_symmetric(data):
     P = transformer.get_penalty_matrix()
     assert P.shape[0] == P.shape[1]
     assert np.allclose(P, P.T, atol=1e-9)
+
+
+# --------------------------------------------------------------------------- #
+# A partition-of-unity basis must not carry a redundant intercept column.
+#
+# ``BSplineTransformer`` used to default to ``include_bias=True``. A B-spline
+# basis over a clamped knot vector sums to 1 on every row, so the prepended
+# column of ones is an exact linear combination of the rest and the design
+# matrix is singular (condition number ~1e15).
+# --------------------------------------------------------------------------- #
+def test_bspline_default_design_is_full_rank():
+    X = np.linspace(0, 1, 200).reshape(-1, 1)
+
+    design = BSplineTransformer(output_dim=8).fit_transform(X)
+
+    assert design.shape[1] == 8
+    assert np.linalg.matrix_rank(design) == design.shape[1]
+    assert np.linalg.cond(design) < 1e6
+
+
+def test_bspline_basis_is_a_partition_of_unity():
+    # This is *why* the bias column is redundant; pin it so the reasoning holds.
+    X = np.linspace(0, 1, 200).reshape(-1, 1)
+
+    design = BSplineTransformer(output_dim=8).fit_transform(X)
+
+    np.testing.assert_allclose(design.sum(axis=1), 1.0)
+
+
+def test_bspline_include_bias_still_available_opt_in():
+    X = np.linspace(0, 1, 200).reshape(-1, 1)
+
+    design = BSplineTransformer(output_dim=8, include_bias=True).fit_transform(X)
+
+    assert design.shape[1] == 9
+    np.testing.assert_allclose(design[:, 0], 1.0)
+
+
+@pytest.mark.parametrize("cls", [BSplineTransformer, MSplineTransformer, ISplineTransformer])
+def test_bmi_splines_default_to_exactly_output_dim(cls):
+    X = np.linspace(0, 1, 200).reshape(-1, 1)
+
+    assert cls(output_dim=7).fit_transform(X).shape[1] == 7