diff --git a/xopt/generators/bayesian/turbo.py b/xopt/generators/bayesian/turbo.py
index 72a8c696..63cc99fd 100644
--- a/xopt/generators/bayesian/turbo.py
+++ b/xopt/generators/bayesian/turbo.py
@@ -256,10 +256,13 @@ def get_trust_region(self, generator: "BayesianGenerator") -> Tensor:
                     if active_indices:
                         lengthscales = lengthscales[active_indices]
 
-                    # calculate the ratios of lengthscales for each axis
+                    # calculate the ratios of lengthscales for each axis,
+                    # taking the per-element root before multiplying so the
+                    # product cannot overflow/underflow for extreme
+                    # lengthscales (e.g. degenerate fits in high dimensions)
                     active_dim = len(active_variable_names)
-                    weights = lengthscales / torch.prod(lengthscales) ** (
-                        1 / active_dim
+                    weights = lengthscales / torch.prod(
+                        lengthscales ** (1 / active_dim)
                     )
 
             # calculate the tr bounding box
diff --git a/xopt/tests/generators/bayesian/test_turbo.py b/xopt/tests/generators/bayesian/test_turbo.py
index ee0208e3..a4f4d9ef 100644
--- a/xopt/tests/generators/bayesian/test_turbo.py
+++ b/xopt/tests/generators/bayesian/test_turbo.py
@@ -7,6 +7,7 @@
 import numpy as np
 import pandas as pd
 import pytest
+import torch
 import yaml
 
 from gest_api.vocs import VOCS
@@ -594,3 +595,53 @@ def clean_up(self):
         for f in files:
             if os.path.exists(f):
                 os.remove(f)
+
+
+# Lives outside TestTurbo because pytest cannot parametrize unittest.TestCase
+# methods -- parametrization is fixture-driven and TestCase methods take no
+# fixtures, so the decorator would leave the argument unfilled at call time.
+@pytest.mark.parametrize(
+    "lengthscale",
+    [pytest.param(1.0e200, id="overflow"), pytest.param(1.0e-200, id="underflow")],
+)
+def test_get_trust_region_extreme_lengthscales(lengthscale):
+    # The geometric-mean normalization must survive lengthscales at both
+    # extremes. With the naive prod(ls) ** (1 / d) form the raw product is
+    # unrepresentable in either direction, and the trust region degenerates
+    # silently -- no warning, no NaN, no exception:
+    #   huge ls -> prod overflows to inf -> weights 0   -> region collapses
+    #                                                      to the center point
+    #   tiny ls -> prod underflows to 0  -> weights inf -> region is clamped
+    #                                                      out to the whole domain
+    # The underflow case is why "finite, with nonzero width" does not pin this
+    # on its own: a region spanning the entire domain satisfies both.
+    test_vocs = deepcopy(TEST_VOCS_BASE)
+    gen = UpperConfidenceBoundGenerator(vocs=test_vocs)
+    gen.add_data(TEST_VOCS_DATA)
+    gen.train_model()
+
+    gen.model.models[0].covar_module.lengthscale = torch.tensor(
+        [[lengthscale, lengthscale]], dtype=torch.double
+    )
+
+    turbo_state = OptimizeTurboController(vocs=gen.vocs)
+    turbo_state.update_state(gen)
+    tr = turbo_state.get_trust_region(gen)
+
+    assert torch.all(torch.isfinite(tr))
+
+    # Equal lengthscales normalize to unit weights, so the region spans at most
+    # `length` of each dimension's full width. Bounding rather than pinning the
+    # width keeps this robust to the clamp in get_trust_region, which
+    # legitimately narrows a side when the incumbent sits near a bound.
+    bounds = torch.tensor(np.array(test_vocs.bounds).T, dtype=torch.double)
+    widths = tr[1] - tr[0]
+    max_widths = turbo_state.length * (bounds[1] - bounds[0])
+
+    assert torch.all(widths > 0.0), (
+        f"region collapsed to a point, widths {widths.tolist()}"
+    )
+    assert torch.all(widths <= max_widths + 1e-12), (
+        f"region blown out past the trust region, widths "
+        f"{widths.tolist()} exceed {max_widths.tolist()}"
+    )