diff --git a/image_analysis/structure_refinement/MolecularReplacement.cpp b/image_analysis/structure_refinement/MolecularReplacement.cpp
index 23e1b4600..971f91405 100644
--- a/image_analysis/structure_refinement/MolecularReplacement.cpp
+++ b/image_analysis/structure_refinement/MolecularReplacement.cpp
@@ -459,11 +459,14 @@ gemmi::Fractional centroid(const gemmi::Structure &st) {
 // about its centroid, in standard deviations of the latter: the null model validation builds for a
 // model that claims something (ModelValidation.cpp). An orientation the crystal cannot tell from the
 // placement's - within the rigid body's reach of one of its symmetry classes - is drawn again.
+// With several copies each is turned about its own centroid, all by the same rotation: the copies keep
+// their arrangement, and with it the fit that tNCS gives any model placed parallel at its vector, so that
+// only the model's own orientation is random.
 // `translate`: where given, each replicate is placed where the translation function puts the model in its
 // orientation (the centroids, fractional, of the model in each of the orientations given), as the search
 // placed the real one, instead of at the real placement's centroid; the search chose that position among
 // all others for the real orientation, and a null that is not given the same choice reads high.
-double null_sigma(const gemmi::Structure &placed, const gemmi::Mat33 &orientation, const gemmi::SpaceGroup &sg,
+double null_sigma(const gemmi::Structure &placed, int copies, const gemmi::Mat33 &orientation, const gemmi::SpaceGroup &sg,
                   const std::vector<MergedReflection> &merged, double d_min, RigidBodyGPUPool *pool,
                   size_t nthreads, ScoreEngines *scorers,
                   const std::function<std::vector<gemmi::Fractional>(const std::vector<gemmi::Mat33> &)> &translate) {
@@ -497,15 +500,23 @@ double null_sigma(const gemmi::Structure &placed, const gemmi::Mat33 &orientatio
         workers.push_back(std::async(std::launch::async, [&] {
             for (int i = next++; i < NULL_REPLICATES; i = next++) {
                 gemmi::Structure rep = placed;
-                std::vector<gemmi::Position> pos = ModelPositions(rep.models[0]);
-                gemmi::Vec3 c;
-                for (const gemmi::Position &p : pos)
-                    c += p;
-                c *= 1.0 / static_cast<double>(pos.size());
-                const gemmi::Vec3 to = translate ? gemmi::Vec3(placed.cell.orthogonalize(where[i])) : c;
-                for (gemmi::Position &p : pos)
-                    p = gemmi::Position(draws[i].multiply(gemmi::Vec3(p) - c) + to);
-                SetModelPositions(rep.models[0], pos);
+                std::vector<gemmi::Chain> &chains = rep.models[0].chains;
+                for (int k = 0; k < copies; k++) {
+                    // Copy k: the chains SplitCopies gives it.
+                    std::vector<gemmi::Atom *> atoms;
+                    for (size_t ch = 0; ch < chains.size(); ch++)
+                        if (static_cast<int>(ch * copies / chains.size()) == k)
+                            for (gemmi::Residue &r : chains[ch].residues)
+                                for (gemmi::Atom &a : r.atoms)
+                                    atoms.push_back(&a);
+                    gemmi::Vec3 c;
+                    for (const gemmi::Atom *a : atoms)
+                        c += a->pos;
+                    c *= 1.0 / static_cast<double>(atoms.size());
+                    const gemmi::Vec3 to = translate ? gemmi::Vec3(placed.cell.orthogonalize(where[i])) : c;
+                    for (gemmi::Atom *a : atoms)
+                        a->pos = gemmi::Position(draws[i].multiply(gemmi::Vec3(a->pos) - c) + to);
+                }
                 r_work[i] = refine_placement(rep, sg, coarse, null_d_min, pool, nthreads, scorers).r_work;
             }
         }));
@@ -2440,7 +2451,7 @@ MolecularReplacementResult search_model(const SearchModel &model, const std::vec
                         out.push_back(p.t);
                     return out;
                 };
-            c.null_sigma = null_sigma(*c.placed, orientations[best], c.space_group, *merges[merge].merged,
+            c.null_sigma = null_sigma(*c.placed, c.copies, orientations[best], c.space_group, *merges[merge].merged,
                                       result.d_min_score, engines.get(), nthreads, &scorers, translate);
             result.t_null += seconds_since(t_null);
             if (c.null_sigma >= NULL_SIGMA_MIN)