diff --git a/rugnux/RugnuxFirstPass.cpp b/rugnux/RugnuxFirstPass.cpp
index 08166d5a4..cc9f06b22 100644
--- a/rugnux/RugnuxFirstPass.cpp
+++ b/rugnux/RugnuxFirstPass.cpp
@@ -1423,11 +1423,14 @@ auto Rugnux::FirstPassRun::IndexSchemes() -> FirstPass {
 // neither the frame count nor the occupancy of the classes it adds tells it from a superstructure.
 // What does is the class of nodes on neither domain. Two domains put every reflection on the union of
 // their own index-n sub-lattices K1 and K2 and leave the (1 - 1/n)^2 of the nodes on neither empty but
-// for chance coincidences. One crystal cannot: whatever sub-lattice its reflections favour (a
-// pseudo-translation), the nodes off K1 that lie on K2 and those that lie on neither are the same
-// cosets of it, and as dense in spots per node. The two sub-lattices are the same lattice in two
-// orientations, so their cells must also agree. Where all of this holds the stronger domain's own
-// cell is adopted, and the other domain is left to the leftover-lattice census, which names it.
+// for chance coincidences, while the nodes on both (the overlap) and on each alone are populated. One
+// crystal cannot do that: whatever sub-lattice its reflections favour (a pseudo-translation), the
+// nodes off K1 that lie on K2 and those that lie on neither are the same cosets of it and as dense in
+// spots, and a crystal whose spots avoid one coset of a sub-lattice thins the overlap with the class
+// on neither alike. So the class on neither must be far emptier than every other class. The two
+// sub-lattices are the same lattice in two orientations, so their cells must also agree. Where all
+// of this holds the stronger domain's own cell is adopted, and the other domain is left to the
+// leftover-lattice census, which names it.
 // Following Friedel's twin index (Friedel 1926, Lecons de cristallographie) and the obverse/reverse
 // reflection classes of Herbst-Irmer & Sheldrick (2002) Acta Cryst. B58, 477-481
 auto Rugnux::FirstPassRun::TwinCompositeHypothesis(FirstPass best) -> FirstPass {
@@ -1482,19 +1485,20 @@ auto Rugnux::FirstPassRun::TwinCompositeHypothesis(FirstPass best) -> FirstPass
         const bool congruent = std::abs(u1.a - u2.a) < 0.02 * u1.a && std::abs(u1.b - u2.b) < 0.02 * u1.b
                                && std::abs(u1.c - u2.c) < 0.02 * u1.c && std::abs(u1.alpha - u2.alpha) < 2.0
                                && std::abs(u1.beta - u2.beta) < 2.0 && std::abs(u1.gamma - u2.gamma) < 2.0;
-        // Spots per node: each domain alone holds 1/n - 1/n^2 of the nodes, neither (1 - 1/n)^2. One
-        // crystal reads the two densities alike, up to the scatter of the pair picked as the emptiest
-        // out of 7 or 13 forms (up to 1.6 where the run has a hundred spots); two domains read them
-        // tens of times apart.
-        const double weak_density = c.only2 / (1.0 / n - 1.0 / (n * n));
+        // Spots per node: each domain alone holds 1/n - 1/n^2 of the nodes, both 1/n^2, neither
+        // (1 - 1/n)^2. One crystal reads the emptiest of the first three about as dense as neither (up
+        // to 1.5 times, the scatter of picking the emptiest pair out of 7 or 13 forms); two domains read
+        // it tens of times denser.
+        const double other_density = std::min(c.only2 / (1.0 / n - 1.0 / (n * n)),
+                                              c.both * static_cast<double>(n * n));
         const double neither_density = c.neither / ((1.0 - 1.0 / n) * (1.0 - 1.0 / n));
-        const bool composite = congruent && c.only2 >= 20 && weak_density > 4.0 * neither_density;
+        const bool composite = congruent && c.only2 >= 20 && other_density > 4.0 * neither_density;
         logger.Info("Twin-composite hypothesis, index {}: of {} validation spots on the standing cell "
                     "({:.0f} A^3), the sub-lattices ({},{},{}) and ({},{},{}) hold {} and {} alone, {} "
-                    "together and {} on neither - per node {:.1f} on the weaker one's own class against "
+                    "together and {} on neither - per node {:.1f} on the emptiest of the other classes against "
                     "{:.1f} on neither{} => {}", n, hkl.size(), best.vol,
                     forms[bi][0], forms[bi][1], forms[bi][2], forms[bj][0], forms[bj][1], forms[bj][2],
-                    c.only1, c.only2, c.both, c.neither, weak_density, neither_density,
+                    c.only1, c.only2, c.both, c.neither, other_density, neither_density,
                     congruent ? "" : ", cells not congruent",
                     composite ? "two domains on their coincidence lattice" : "one lattice");
         if (!composite)