diff --git a/qpms/scatsystem.c b/qpms/scatsystem.c
index 900d5c8..fc3e708 100644
--- a/qpms/scatsystem.c
+++ b/qpms/scatsystem.c
@@ -400,6 +400,7 @@ static void add_orbit_type(qpms_scatsys_t *ss, const qpms_ss_orbit_type_t *ot_cu
         "The cumulative size of the symmetry-adapted bases is wrong; "
         "expected %d = %d * %d, got %d.",
         ot_new->size * bspecn, ot_new->size, bspecn, bs_cumsum);
+  ot_new->instance_count = 0;
 }
 
 
@@ -580,7 +581,9 @@ qpms_scatsys_t *qpms_scatsys_apply_symmetry(const qpms_scatsys_t *orig, const qp
         const qpms_ss_pi_t pi_opi = current_orbit[opi];
         ss->p_orbitinfo[pi_opi].t = oti;
         ss->p_orbitinfo[pi_opi].p = opi;
+        ss->p_orbitinfo[pi_opi].osn = ss->orbit_types[oti].instance_count;
       }
+      ss->orbit_types[oti].instance_count++;
     }
   }
   // Possibly free some space using the new ss->p_count instead of (old) ss->p_count*sym->order
diff --git a/qpms/scatsystem.h b/qpms/scatsystem.h
index f1f2438..4cafecd 100644
--- a/qpms/scatsystem.h
+++ b/qpms/scatsystem.h
@@ -352,13 +352,15 @@ typedef struct qpms_ss_orbit_type_t {
 	 * TODO doc.
 	 */
 	complex double *irbases;
-	
+	/// TODO doc.
+	size_t instance_count;
 } qpms_ss_orbit_type_t;
 
 /// Auxillary type used in qpms_scatsys_t that identifies the particle's orbit and its id inside that orbit.
 typedef struct qpms_ss_particle_orbitinfo {
 	qpms_ss_oti_t t; ///< Orbit type.
 #define QPMS_SS_P_ORBITINFO_UNDEF (-1) ///< This labels that the particle has not yet been assigned to an orbit.
+	ptrdiff_t osn; ///< "Serial number" of the orbit in the given type. TODO type and more doc.
 	qpms_ss_orbit_pi_t p; ///< Order (sija, ei rankki) of the particle inside that orbit type.
 } qpms_ss_particle_orbitinfo_t;