diff --git a/image_analysis/IndexAndRefine.cpp b/image_analysis/IndexAndRefine.cpp
index 82598783..d436f2a7 100644
--- a/image_analysis/IndexAndRefine.cpp
+++ b/image_analysis/IndexAndRefine.cpp
@@ -120,14 +120,16 @@ IndexAndRefine::IndexingOutcome IndexAndRefine::DetermineLatticeAndSymmetry(Data
                 outcome.lattice_candidate = sym_result.conventional;
             }
 
-            // Multi-lattice search for stills: keep extra lattices that share the
-            // reference unit cell but differ only in orientation. Quick refinement
-            // (orientation only) is done later in RefineGeometryIfNeeded.
+            // Multi-lattice search for stills: store rotations that map the reference
+            // lattice to each accepted extra lattice. Candidates are materialized later
+            // in RefineGeometryIfNeeded so they're rooted in the refined (and, for
+            // monoclinic, reordered) main lattice.
             if (indexer_result.lattice.size() > 1) {
                 auto ml_latt = MultiLatticeSearch(indexer_result.lattice);
                 for (auto &ml : ml_latt) {
-                    if (outcome.extra_lattice_candidates.size() >= experiment.GetIndexingSettings().GetMaxExtraLattices())
+                    if (outcome.extra_lattice_rotations.size() >= experiment.GetIndexingSettings().GetMaxExtraLattices())
                         break;
+                    outcome.extra_lattice_rotations.push_back(ml.rotation_vector);
                     RotMatrix rot(ml.rotation_vector.Length(), ml.rotation_vector.Normalize());
                     outcome.extra_lattice_candidates.push_back(outcome.lattice_candidate->Multiply(rot));
                 }
@@ -186,6 +188,17 @@ void IndexAndRefine::RefineGeometryIfNeeded(DataMessage &msg, IndexAndRefine::In
     if (outcome.symmetry.crystal_system == gemmi::CrystalSystem::Monoclinic)
         outcome.lattice_candidate->ReorderMonoclinic();
 
+    // Rebuild extra-lattice candidates from the refined (and possibly reordered) main
+    // lattice so they share its cell and obtuse-beta convention.
+    if (!outcome.extra_lattice_rotations.empty()) {
+        outcome.extra_lattice_candidates.clear();
+        outcome.extra_lattice_candidates.reserve(outcome.extra_lattice_rotations.size());
+        for (const auto &rv : outcome.extra_lattice_rotations) {
+            RotMatrix rot(rv.Length(), rv.Normalize());
+            outcome.extra_lattice_candidates.push_back(outcome.lattice_candidate->Multiply(rot));
+        }
+    }
+
     // Quick orientation-only refinement of extra lattices (stills path).
     // Cell, beam center, detector geometry are taken from the first lattice.
     if (!experiment.IsRotationIndexing() && !outcome.extra_lattice_candidates.empty()) {
diff --git a/image_analysis/IndexAndRefine.h b/image_analysis/IndexAndRefine.h
index 8df60d21..0f03ee97 100644
--- a/image_analysis/IndexAndRefine.h
+++ b/image_analysis/IndexAndRefine.h
@@ -36,6 +36,7 @@ class IndexAndRefine {
     struct IndexingOutcome {
         std::optional<CrystalLattice> lattice_candidate;
         std::vector<CrystalLattice> extra_lattice_candidates;
+        std::vector<Coord> extra_lattice_rotations;
         DiffractionExperiment experiment;
         LatticeMessage symmetry{
             .centering = 'P',
diff --git a/image_analysis/indexing/MultiLatticeSearch.cpp b/image_analysis/indexing/MultiLatticeSearch.cpp
index 3080fc31..d40bc3fb 100644
--- a/image_analysis/indexing/MultiLatticeSearch.cpp
+++ b/image_analysis/indexing/MultiLatticeSearch.cpp
@@ -3,6 +3,9 @@
 
 #include "MultiLatticeSearch.h"
 
+#include <array>
+#include <vector>
+
 #include <Eigen/Dense>
 
 namespace {
@@ -33,30 +36,42 @@ namespace {
         }
         return R;
     }
-}
 
-CrystalLattice Transform(const CrystalLattice &in_latt, int i) {
-    CrystalLattice latt = in_latt;
-    switch (i) {
-        case 0:
-            break;
-        case 1:
-            latt.FlipSign(0);
-            latt.FlipSign(1);
-            break;
-        case 2:
-            latt.FlipSign(0);
-            latt.FlipSign(2);
-            break;
-        case 3:
-            latt.FlipSign(1);
-            latt.FlipSign(2);
-            break;
-        default:
-            break;
+    struct BasisOp {
+        std::array<int, 3> perm;
+        std::array<int, 3> signs; // each +1 or -1
+    };
+
+    // The 24 right-handed (det=+1) sign+permutation reparametrizations of a basis (a,b,c).
+    // Identity (perm 0,1,2; signs +,+,+) is first so it's preferred when several ops match
+    // the reference cell. For low-symmetry cells, only a handful pass is_close; for cubic,
+    // all 24 may pass and the first-match rule keeps behavior deterministic.
+    const std::vector<BasisOp> &RightHandedOps() {
+        static const std::vector<BasisOp> ops = []() {
+            std::vector<BasisOp> v;
+            const std::array<std::array<int, 3>, 6> perms = {{
+                {0, 1, 2}, {1, 2, 0}, {2, 0, 1}, // even
+                {0, 2, 1}, {2, 1, 0}, {1, 0, 2}  // odd
+            }};
+            for (size_t p = 0; p < perms.size(); p++) {
+                const int parity = (p < 3) ? +1 : -1;
+                for (int s0 : {+1, -1})
+                    for (int s1 : {+1, -1})
+                        for (int s2 : {+1, -1})
+                            if (parity * s0 * s1 * s2 == +1)
+                                v.push_back({perms[p], {s0, s1, s2}});
+            }
+            return v;
+        }();
+        return ops;
     }
 
-    return latt;
+    CrystalLattice ApplyBasisOp(const CrystalLattice &in, const BasisOp &op) {
+        const Coord v[3] = {in.Vec0(), in.Vec1(), in.Vec2()};
+        return CrystalLattice(v[op.perm[0]] * static_cast<float>(op.signs[0]),
+                              v[op.perm[1]] * static_cast<float>(op.signs[1]),
+                              v[op.perm[2]] * static_cast<float>(op.signs[2]));
+    }
 }
 
 std::vector<MultiLatticeSearchResult> MultiLatticeSearch(const std::vector<CrystalLattice> &lattices,
@@ -70,9 +85,8 @@ std::vector<MultiLatticeSearchResult> MultiLatticeSearch(const std::vector<Cryst
     const UnitCell ref_cell = reference.GetUnitCell();
 
     for (size_t i = 1; i < lattices.size(); i++) {
-        bool found = false;
-        for (int flip = 0; flip < 4; flip++) {
-            const CrystalLattice latt = Transform(lattices[i], flip);
+        for (const auto &op : RightHandedOps()) {
+            const CrystalLattice latt = ApplyBasisOp(lattices[i], op);
 
             if (!latt.GetUnitCell().is_close(ref_cell, dist_tolerance, angle_tolerance_deg))
                 continue;
@@ -81,14 +95,10 @@ std::vector<MultiLatticeSearchResult> MultiLatticeSearch(const std::vector<Cryst
 
             const Eigen::AngleAxisd aa(R);
             const Eigen::Vector3d rod = aa.angle() * aa.axis();
-            const Coord rotation_vector(static_cast<float>(rod.x()),
-                                        static_cast<float>(rod.y()),
-                                        static_cast<float>(rod.z()));
-
-            if (found)
-                continue;
-            ret.push_back({rotation_vector});
-            found = true;
+            ret.push_back({Coord(static_cast<float>(rod.x()),
+                                 static_cast<float>(rod.y()),
+                                 static_cast<float>(rod.z()))});
+            break;
         }
     }