diff --git a/pyproject.toml b/pyproject.toml
index 868a701..b0869b1 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@ build-backend = "hatchling.build"
 
 [project]
 name = "nlls-gram"
-version = "2.7.0"
+version = "2.8.0"
 description = "Metric-aware Levenberg-Marquardt nonlinear least-squares for JAX"
 readme = "README.md"
 license = "MIT"
diff --git a/src/nlls_gram/multi_start.py b/src/nlls_gram/multi_start.py
index d420473..0da9263 100644
--- a/src/nlls_gram/multi_start.py
+++ b/src/nlls_gram/multi_start.py
@@ -92,7 +92,9 @@ class DrawNNXModule:
 
     Given a ``MultiStart`` retry key, builds
     ``module_cls(*args, rngs=nnx.Rngs(key), **kwargs)`` and returns its ``nnx.Param``
-    state as the new solver start, passing ``args`` through unchanged. Use it instead
+    state as the new solver start, passing ``args`` through unchanged. Non-``Param``
+    Variables (scaling constants, statistics) are excluded from the drawn state --
+    the residual's ``nnx.merge`` supplies them alongside the graphdef. Use it instead
     of hand-rolling a re-init closure per driver::
 
         draw = DrawNNXModule(SequentialMLP, settings, dtype=dtype)
@@ -122,7 +124,7 @@ def __call__(self, key, x_old, args_old):
         from flax import nnx
 
         module = self.module_cls(*self.args, rngs=nnx.Rngs(key), **dict(self.kwargs))
-        _, theta = nnx.split(module, nnx.Param)
+        _, theta, _ = nnx.split(module, nnx.Param, ...)
         return theta, args_old
 
     def __hash__(self):
diff --git a/tests/test_nnx_gram_lm.py b/tests/test_nnx_gram_lm.py
index b0023c9..11d1b33 100644
--- a/tests/test_nnx_gram_lm.py
+++ b/tests/test_nnx_gram_lm.py
@@ -236,6 +236,43 @@ def run(draw):
         assert jnp.allclose(got, want)
 
 
+class ScaledCurveMLP(nnx.Module):
+    def __init__(self, *, scale=2.0, rngs: nnx.Rngs):
+        self.scale = nnx.Variable(jnp.asarray(scale))
+        self.hidden = nnx.Linear(1, 8, rngs=rngs)
+        self.head = nnx.Linear(8, 1, rngs=rngs)
+
+    def __call__(self, x):
+        return self.scale[...] * self.head(nnx.tanh(self.hidden(x[:, None])))[:, 0]
+
+
+def test_draw_nnx_module_excludes_non_param_variables():
+    graphdef, theta_0, nondiff = nnx.split(
+        ScaledCurveMLP(rngs=nnx.Rngs(1)), nnx.Param, ...
+    )
+    assert len(jax.tree.leaves(nondiff)) == 1
+
+    draw = DrawNNXModule(ScaledCurveMLP)
+    theta, args_out = draw(jax.random.key(7), None, ("args",))
+    assert args_out == ("args",)
+    # Only the Param leaves are drawn; the residual's merge supplies nondiff.
+    assert jax.tree_util.tree_structure(theta) == jax.tree_util.tree_structure(theta_0)
+
+    ts = jnp.linspace(-1.0, 1.0, 32)
+    ys = jnp.sin(2.0 * ts)
+    theta_bad = jax.tree.map(lambda leaf: leaf * jnp.nan, theta_0)
+
+    def residual(theta, args, p):
+        ts, ys = args
+        return nnx.merge(graphdef, theta, nondiff)(ts) - ys
+
+    solver = LevenbergMarquardt(residual, init_damping=1e-2)
+    ms = MultiStart(key=jax.random.key(2), num_starts=4, draw=draw)
+    result = solver.solve(theta_bad, (ts, ys), max_steps=200, atol=5e-3, multi_start=ms)
+    assert int(result.status) == LMStatus.CONVERGED
+    assert bool(result.multi_start.accepted)
+
+
 @pytest.mark.parametrize("parallel", [False, True])
 def test_multi_start_draw_nnx_module_recovers_from_bad_init(parallel):
     ts = jnp.linspace(-1.0, 1.0, 32)
diff --git a/uv.lock b/uv.lock
index 2aff017..0fd1bbb 100644
--- a/uv.lock
+++ b/uv.lock
@@ -726,7 +726,7 @@ wheels = [
 
 [[package]]
 name = "nlls-gram"
-version = "2.7.0"
+version = "2.8.0"
 source = { editable = "." }
 dependencies = [
     { name = "jax" },