diff --git a/image_analysis/lattice_search/LatticeSearch.cpp b/image_analysis/lattice_search/LatticeSearch.cpp
index fbeb22a6..d8e5e85a 100644
--- a/image_analysis/lattice_search/LatticeSearch.cpp
+++ b/image_analysis/lattice_search/LatticeSearch.cpp
@@ -8,6 +8,15 @@
 #include <cmath>
 #include <optional>
 
+// How close the reduced beta has to be to 90 degrees for the two Niggli types to be genuinely
+// interchangeable (see the retry at the end of LatticeSearch). Not the angle tolerance: that is how
+// far a metric may sit from an ideal one and still be called it, which is far too generous here - a
+// cell 2 degrees off the boundary is a real type-1 cell, and presenting it in the obtuse setting
+// promotes a general triclinic lattice to C-centred monoclinic on residuals of ~2 degrees. Measured:
+// the crystal this was found on sits 0.07 degrees from the boundary and matches on 0.006 to 0.135;
+// the triclinic cell that must not be promoted sits 2.0 degrees from it.
+constexpr double NIGGLI_TYPE_BOUNDARY_DEG = 0.5;
+
 struct NiggliClass {
     int number;
     int type;
@@ -352,10 +361,12 @@ LatticeSearchResult LatticeSearch(const CrystalLattice &L, double dist_tolerance
         return std::nullopt;
     };
 
-    if (auto found = match(L_niggli, D, E, F))
+    // Character 44 fits any cell, so a match is always found - "nothing fits" is reported as triclinic.
+    auto found = match(L_niggli, D, E, F);
+    if (found && found->system != gemmi::CrystalSystem::Triclinic)
         return *found;
 
-    // A reduced cell whose beta is 90 to within the angle tolerance sits ON the boundary between the two
+    // A reduced cell whose beta is 90 to within NIGGLI_TYPE_BOUNDARY_DEG sits ON the boundary between the two
     // Niggli types: the same lattice reduces to an all-acute cell or an all-obtuse one according to the
     // last digits of whatever refinement produced it. The type-1 characters are skipped for such a cell
     // (just above) and the type-2 ones are stated for the obtuse setting, so an acute cell can match none
@@ -363,12 +374,16 @@ LatticeSearchResult LatticeSearch(const CrystalLattice &L, double dist_tolerance
     // and c keeps the lattice and beta and turns alpha and gamma into their supplements. Measured on a
     // C-centred monoclinic crystal whose reduced beta sits 0.07 deg from 90: its centring was read or
     // missed according to the sign of that 0.07 deg, and with it the space group of the whole run.
-    if (L_niggli.GetUnitCell().beta >= 90 - angle_tolerance && D > 0 && E > 0 && F > 0) {
+    if (L_niggli.GetUnitCell().beta >= 90 - NIGGLI_TYPE_BOUNDARY_DEG && D > 0 && E > 0 && F > 0) {
         const gemmi::Mat33 obtuse(-1, 0, 0, 0, 1, 0, 0, 0, -1);
-        if (auto found = match(L_niggli.Multiply(obtuse), -D, E, -F))
-            return *found;
+        const auto flipped = match(L_niggli.Multiply(obtuse), -D, E, -F);
+        if (flipped && flipped->system != gemmi::CrystalSystem::Triclinic)
+            return *flipped;
     }
 
+    if (found)
+        return *found;
+
     return LatticeSearchResult{
         .niggli_class = 44,
         .primitive_reduced = L_niggli,