diff --git a/rugnux/RigidBodyRefine.cpp b/rugnux/RigidBodyRefine.cpp
index 8b36f44d5..e60339c57 100644
--- a/rugnux/RigidBodyRefine.cpp
+++ b/rugnux/RigidBodyRefine.cpp
@@ -214,8 +214,17 @@ public:
 
     bool Evaluate(double const *const *parameters, double *residuals, double **jacobians) const override {
         const int n = num_residuals();
-        if (!ev_.Residuals(parameters[0], residuals))
-            return false;
+        // Ceres evaluates every step it accepts twice: the residuals alone to decide whether to take
+        // it, then residuals and Jacobian together at the same point. The residuals are a function of
+        // the placement alone, so the second time they are the first time's, copied.
+        if (!last_residuals_.empty() && std::equal(parameters[0], parameters[0] + 6, last_q_.begin())) {
+            std::copy(last_residuals_.begin(), last_residuals_.end(), residuals);
+        } else {
+            if (!ev_.Residuals(parameters[0], residuals))
+                return false;
+            std::copy(parameters[0], parameters[0] + 6, last_q_.begin());
+            last_residuals_.assign(residuals, residuals + n);
+        }
         if (jacobians != nullptr && jacobians[0] != nullptr) {
             const double step = ev_.JacobianStep();
             std::vector<std::vector<double>> shifted(6, std::vector<double>(n));
@@ -244,6 +253,8 @@ private:
     Evaluator &ev_;
     std::vector<Evaluator> &columns_;
     size_t nthreads_;
+    mutable std::array<double, 6> last_q_{};
+    mutable std::vector<double> last_residuals_;   // at last_q_; empty until an evaluation succeeds
 };
 
 // The directions in which this space group's origin is free. Translating the whole cell content along