diff --git a/image_analysis/structure_refinement/ModelScaleGPU.cu b/image_analysis/structure_refinement/ModelScaleGPU.cu
index de11ff941..35ebf187f 100644
--- a/image_analysis/structure_refinement/ModelScaleGPU.cu
+++ b/image_analysis/structure_refinement/ModelScaleGPU.cu
@@ -373,6 +373,14 @@ struct ModelScaleGPU::LevMarRun {
             done = true;
             return;
         }
+        // As LevMarFit (ModelScaling.cpp): a fit that has walked to where k_overall exp(-B s^2) |F| underflows at
+        // every reflection has no step left - the squares in alpha are all 0 while beta keeps a residue, and the
+        // solve throws on that. It ends here, at its best so far. J^T J is summed in float, so its squares
+        // underflow once |F| k_aniso is below about 1e-22 everywhere, still far from any scale a fit can end at.
+        if (alpha[0] == 0) {
+            done = true;
+            return;
+        }
         const size_t na = beta.size();
         std::vector<double> temp_alpha = alpha;
         for (size_t j = 0; j < na; j++)