typedef struct rev_name {
        const char *tip_name;
-       int merge_traversals;
        int generation;
+       int distance;
 } rev_name;
 
 static long cutoff = LONG_MAX;
 
+/* How many generations are maximally preferred over _one_ merge traversal? */
+#define MERGE_TRAVERSAL_WEIGHT 65535
+
 static void name_rev(struct commit *commit,
-               const char *tip_name, int merge_traversals, int generation,
+               const char *tip_name, int generation, int distance,
                int deref)
 {
        struct rev_name *name = (struct rev_name *)commit->util;
                name = xmalloc(sizeof(rev_name));
                commit->util = name;
                goto copy_data;
-       } else if (name->merge_traversals > merge_traversals ||
-                       (name->merge_traversals == merge_traversals &&
-                        name->generation > generation)) {
+       } else if (name->distance > distance) {
 copy_data:
                name->tip_name = tip_name;
-               name->merge_traversals = merge_traversals;
                name->generation = generation;
+               name->distance = distance;
        } else
                return;
 
                                sprintf(new_name, "%.*s^%d", len, tip_name,
                                                parent_number);
 
-                       name_rev(parents->item, new_name,
-                               merge_traversals + 1 , 0, 0);
+                       name_rev(parents->item, new_name, 0,
+                               distance + MERGE_TRAVERSAL_WEIGHT, 0);
                } else {
-                       name_rev(parents->item, tip_name, merge_traversals,
-                               generation + 1, 0);
+                       name_rev(parents->item, tip_name, generation + 1,
+                               distance + 1, 0);
                }
        }
 }