diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index b5eda98c1..b181deb0b 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -13,6 +13,7 @@
 * The `rugnux` report gives the twinning statistics measured before the space group was decided, beside the ones measured after.
 * The `rugnux` report gives the strong-direction diffraction limit, and warns when CC1/2 is not monotone with resolution.
 * `rugnux` ranks screw axes on the evidence their absences carry, rather than on how many control reflections a candidate happens to have.
+* Twinning is no longer reported when the L-test contradicts it.
 * The `jfjoch_viewer` grid scan view draws the cells in the proportion of the scan steps, so the map has the shape of the scanned area.
 
 ### 1.0.0-rc.165
diff --git a/image_analysis/scale_merge/TwinningAnalysis.cpp b/image_analysis/scale_merge/TwinningAnalysis.cpp
index 56e6fbc4c..26b365e6d 100644
--- a/image_analysis/scale_merge/TwinningAnalysis.cpp
+++ b/image_analysis/scale_merge/TwinningAnalysis.cpp
@@ -195,7 +195,14 @@ TwinningAnalysisResult AnalyzeTwinning(const std::vector<MergedReflection>& merg
     // possible, so a low <|L|> is a statistical artefact (correlated near-neighbours) rather than a
     // twin, and must not be flagged.
     result.merohedral_twinning_possible = MerohedralTwinningPossible(space_group);
-    result.twinning_suspected = result.merohedral_twinning_possible &&
+    // The two indicators can only move one way under twinning: <|L|> down from 0.500 towards 0.375,
+    // the second moment down from 2.0 towards 1.5. A narrow intensity distribution sitting next to an
+    // <|L|> at or ABOVE its untwinned value therefore has some other cause, and calling it a twin is
+    // the one reading the data rule out. It happens on small-cell rotation data, where a twin fraction
+    // of 0.50 was reported for a crystal whose <|L|> was 0.63 - a value a twin cannot produce, and one
+    // that points at the opposite situation, a structure whose intensities behave centric.
+    const bool l_test_contradicts_twin = result.l_test_pairs > 0 && result.mean_abs_l >= 0.50;
+    result.twinning_suspected = result.merohedral_twinning_possible && !l_test_contradicts_twin &&
                                 ((result.l_test_pairs > 0 && result.mean_abs_l < 0.44) ||
                                  (result.moment_reflections > 0 && result.second_moment < 1.85));
     return result;