diff --git a/roughpy_jax/streams/piecewise_abelian_stream.py b/roughpy_jax/streams/piecewise_abelian_stream.py
index 4ebf5b6..bb0bb49 100644
--- a/roughpy_jax/streams/piecewise_abelian_stream.py
+++ b/roughpy_jax/streams/piecewise_abelian_stream.py
@@ -14,13 +14,17 @@
     to_log_signature,
     to_signature,
 )
-from roughpy_jax.bases import LieBasis, TensorBasis, Basis
+from roughpy_jax.bases import Basis, LieBasis, TensorBasis
 from roughpy_jax.intervals import Interval, Partition, RealInterval, intersection
 
 from .concepts import Stream
 
 
-@partial(jax.tree_util.register_dataclass, data_fields=["_data", "_partition"],meta_fields=["_lie_basis", "_group_basis"],)
+@partial(
+    jax.tree_util.register_dataclass,
+    data_fields=["_data", "_partition"],
+    meta_fields=["_lie_basis", "_group_basis"],
+)
 @dataclass(frozen=True)
 class PiecewiseAbelianStream(Stream[DenseLie, DenseFreeTensor]):
     """A stream representing a piecewise abelian path."""
@@ -85,7 +89,9 @@ def log_signature(self, interval: Interval) -> DenseLie:
                 "or single-element endpoint arrays"
             )
         if inf.shape or sup.shape:
-            interval = RealInterval(inf.reshape(()), sup.reshape(()), interval.interval_type)
+            interval = RealInterval(
+                inf.reshape(()), sup.reshape(()), interval.interval_type
+            )
 
         initial = FreeTensor.identity(
             self._group_basis,
@@ -116,20 +122,16 @@ def get_piece(x_and_interval):
             )
 
         intervals = self._partition.to_intervals()
-        all_tensors = [initial] + [
-            get_piece((x, p)) for x, p in zip(self._data, intervals, strict=True)
-        ]
 
         # Stack all tensors along a leading axis into a single batched FreeTensor.
-        batched = jax.tree.map(lambda *arrs: jnp.stack(arrs), *all_tensors)
+        pieces = [get_piece((x, p)) for x, p in zip(self._data, intervals, strict=True)]
+        batched = jax.tree.map(lambda *arrs: jnp.stack(arrs), *pieces)
 
-        result_batched = lax.associative_scan(
-            lambda a, b: ft_fmexp(a, b, self._group_basis),
-            batched,
-        )
+        def combine(carry, piece):
+            updated = ft_fmexp(carry, piece, self._group_basis)
+            return updated, None
 
-        # Take the last prefix (the full product over all selected pieces).
-        result = jax.tree.map(lambda x: x[-1], result_batched)
+        result, _ = lax.scan(combine, initial, batched)
         return to_log_signature(result)
 
     @jax.jit
diff --git a/roughpy_jax/tests/streams/test_piecewise_abelian_stream.py b/roughpy_jax/tests/streams/test_piecewise_abelian_stream.py
index dd87f56..15bb101 100644
--- a/roughpy_jax/tests/streams/test_piecewise_abelian_stream.py
+++ b/roughpy_jax/tests/streams/test_piecewise_abelian_stream.py
@@ -2,6 +2,7 @@
 import jax.numpy as jnp
 import pytest
 import roughpy_jax as rpj
+from roughpy_jax.algebra import FreeTensor, ft_fmexp, lie_to_tensor, to_log_signature
 from roughpy_jax.intervals import IntervalType, Partition, RealInterval
 from roughpy_jax.streams import PiecewiseAbelianStream
 
@@ -119,6 +120,38 @@ def test_log_signature_cbh(self, pas_data):
 
         assert jnp.allclose(log_sig.data, expected_log_sig.data, atol=1e-6)
 
+    def test_log_signature_multi_piece_stream(self):
+        lie_basis = rpj.LieBasis(26, 3)
+        tensor_basis = rpj.to_tensor_basis(lie_basis)
+        indices = (0, 1, 4, 19)
+
+        def make_lie(index):
+            data = jnp.zeros((lie_basis.size(),), dtype=jnp.float32)
+            data = data.at[index].set(1.0)
+            return rpj.Lie(data, lie_basis)
+
+        lies = tuple(make_lie(index) for index in indices)
+        stream = PiecewiseAbelianStream(
+            _data=lies,
+            _partition=Partition([0.0, 1.0, 2.0, 3.0, 4.0], IntervalType.ClOpen),
+            _lie_basis=lie_basis,
+            _group_basis=tensor_basis,
+        )
+        query_interval = RealInterval(0.0, 4.0, IntervalType.ClOpen)
+
+        actual_log_sig = stream.log_signature(query_interval)
+
+        expected_signature = FreeTensor.identity(tensor_basis, dtype=jnp.float32)
+        for lie in lies:
+            expected_signature = ft_fmexp(
+                expected_signature,
+                lie_to_tensor(lie),
+                tensor_basis,
+            )
+        expected_log_sig = to_log_signature(expected_signature)
+
+        assert jnp.allclose(actual_log_sig.data, expected_log_sig.data, atol=1e-6)
+
     def test_stream_metadata(self, pas_data):
         """Test that the stream exposes dtype and batch metadata."""
         assert pas_data.stream.dtype == pas_data.dtype