diff --git a/funsor/terms.py b/funsor/terms.py
index d5d795ff..49611b2c 100644
--- a/funsor/terms.py
+++ b/funsor/terms.py
@@ -1218,6 +1218,16 @@ def _alpha_convert(self, alpha_subs):
         reduced_vars = frozenset(alpha_subs.get(var.name, var) for var in reduced_vars)
         return op, subs, source, reduced_vars
 
+    def eager_subs(self, subs):
+        subs = OrderedDict(subs)
+        new_subs = []
+        for name, sub in self.subs:
+            if name in subs and isinstance(subs[name], Variable):
+                new_subs.append((subs[name].name, sub))
+            else:
+                new_subs.append((name, sub))
+        return Scatter(self.op, tuple(new_subs), self.source, self.reduced_vars)
+
 
 class Approximate(Funsor):
     """
diff --git a/test/test_tensor.py b/test/test_tensor.py
index 6b4e5323..a2a733f6 100644
--- a/test/test_tensor.py
+++ b/test/test_tensor.py
@@ -14,6 +14,8 @@
 
 import funsor
 import funsor.ops as ops
+from funsor.cnf import Contraction
+from funsor.delta import Delta
 from funsor.domains import Array, Bint, Product, Real, Reals, find_domain
 from funsor.interpretations import eager, lazy
 from funsor.tensor import (
@@ -1468,3 +1470,44 @@ def raw_reduction(x, dim=None, keepdims=False, batch_ndims=len(batch_shape)):
             actual = op(Tensor(data, inputs), dim, keepdims=keepdims)
             expected = Tensor(raw_reduction(data, dim, keepdims), inputs, dtype)
             assert_close(actual, expected, rtol=rtol)
+
+
+def test_scatter_substitute():
+    expr = Scatter(
+        ops.logaddexp,
+        (
+            (
+                "_time_states_38",
+                Number(0, 1),
+            ),
+        ),
+        Contraction(
+            ops.null,
+            ops.add,
+            frozenset(),
+            (
+                Delta(
+                    (
+                        (
+                            "states",
+                            (
+                                Tensor(np.array(5, dtype=np.int32), (), 10),
+                                Number(0.0),
+                            ),
+                        ),
+                        (
+                            "_PREV_states",
+                            (
+                                Tensor(np.array(4, dtype=np.int32), (), 10),
+                                Number(0.0),
+                            ),
+                        ),
+                    )
+                ),
+                Tensor(np.array(0.3386716842651367, dtype=np.float32), (), "real"),
+            ),
+        ),
+        frozenset(),
+    )
+
+    expr(_time_states_38="_time_states")