diff --git a/src/mesh.cpp b/src/mesh.cpp
index acd80c7ba..9e27fc4e6 100644
--- a/src/mesh.cpp
+++ b/src/mesh.cpp
@@ -524,6 +524,14 @@ void RegularMesh::bins_crossed(const Particle* p, std::vector<int>& bins,
   }
   r1 = r;
 
+  // The TINY_BIT offsets above mean that the preceding logic cannot always find
+  // the correct ijk0 and ijk1 indices. For tracks shorter than 2*TINY_BIT, just
+  // assume the track lies in only one mesh bin. These tracks are very short so
+  // any error caused by this assumption will be small.
+  if (total_distance < 2*TINY_BIT) {
+    for (int i = 0; i < n; ++i) ijk0[i] = ijk1[i];
+  }
+
   // ========================================================================
   // Find which mesh cells are traversed and the length of each traversal.
 
@@ -899,6 +907,14 @@ void RectilinearMesh::bins_crossed(const Particle* p, std::vector<int>& bins,
   }
   r1 = r;
 
+  // The TINY_BIT offsets above mean that the preceding logic cannot always find
+  // the correct ijk0 and ijk1 indices. For tracks shorter than 2*TINY_BIT, just
+  // assume the track lies in only one mesh bin. These tracks are very short so
+  // any error caused by this assumption will be small.
+  if (total_distance < 2*TINY_BIT) {
+    for (int i = 0; i < 3; ++i) ijk0[i] = ijk1[i];
+  }
+
   // ========================================================================
   // Find which mesh cells are traversed and the length of each traversal.