diff --git a/rugnux/Rugnux.cpp b/rugnux/Rugnux.cpp
index cd54fe056..e35246179 100644
--- a/rugnux/Rugnux.cpp
+++ b/rugnux/Rugnux.cpp
@@ -2017,14 +2017,39 @@ ProcessResult Rugnux::RunPipeline(RugnuxObserver *observer, bool write_output, b
                 // ratio separates a real axis multiplication from a centering coincidence. Volumes are
                 // primitive (see above), so a pure setting difference is a ratio of 1 and never fires.
                 bool integer_subcell = false;
-                if (bp.result.has_value() && !clearly_more && vol > 1.0 && bp.vol > 1.0) {
+                double harmonic_ratio = 0.0;
+                if (bp.result.has_value() && vol > 1.0 && bp.vol > 1.0) {
                     const bool tied = static_cast<float>(score) >= bp.score * 0.9f - 0.5f;
                     const double ratio = (vol < bp.vol) ? bp.vol / vol : vol / bp.vol;
                     const double nearest = std::round(ratio);
                     const bool integer_multiple = nearest >= 2.0 && std::abs(ratio - nearest) < 0.15;
-                    integer_subcell = tied && integer_multiple && vol < bp.vol;
+                    integer_subcell = tied && !clearly_more && integer_multiple && vol < bp.vol;
+                    // sqrt(3) as well as an integer: a hexagonal supercell that lengthens one axis by
+                    // sqrt(3) is the other harmonic seen on real data and its volume ratio is not a
+                    // whole number. This is a REPORT and not a decision - it is deliberately taken
+                    // over the whole pair, `clearly_more` included, because the harmonic is often the
+                    // one that indexes more frames (see below).
+                    if (integer_multiple || std::abs(ratio - std::sqrt(3.0)) < 0.15)
+                        harmonic_ratio = ratio;
                 }
 
+                // Two candidates whose primitive volumes differ by a small integer or by sqrt(3) are
+                // one lattice and its axis harmonic, and what decides between them is the BEAM CENTRE.
+                // A centre error along the spindle translates the derotated cloud rigidly, which the
+                // FFT amplitude cannot see at all, so the peaks stay sharp and the indexer commits -
+                // with confidence - to a sub-multiple. Measured on real data: a 0.12 px change of
+                // centre, 0.03x of what the J0 law asks across the spindle, is the whole difference
+                // between the deposited cell and a halved axis, and the halved one is the answer that
+                // indexed MORE frames (100.00 % against 99.23 %). So the frame count cannot arbitrate
+                // this pair, and until this line nothing in the run said what the pair meant.
+                if (harmonic_ratio > 0.0)
+                    logger.Warning("Scheme '{}' (primitive cell volume {:.0f} A^3) and '{}' ({:.0f} A^3) "
+                                   "differ by {:.2f}x - one is an axis harmonic of the other. Which of "
+                                   "the two is right is settled by the beam centre to a fraction of a "
+                                   "pixel, and the harmonic is often the one that indexes MORE frames, "
+                                   "so the frame counts above cannot decide it. Check the beam centre "
+                                   "(--estimate-beam-center)", name, vol, bp.name, bp.vol, harmonic_ratio);
+
                 if (!bp.result.has_value() || clearly_more || integer_subcell) {
                     if (integer_subcell)
                         logger.Info("Scheme '{}' cell (vol {:.0f}) is a {:.0f}x sub-cell of '{}' (vol {:.0f}) at "