diff --git a/kwant/physics/leads.py b/kwant/physics/leads.py
index aadb568b5be2f3b265283d9dff65a8769fd5a3e9..6f58f30d1d0336036690963fc69298fbecd601b3 100644
--- a/kwant/physics/leads.py
+++ b/kwant/physics/leads.py
@@ -124,9 +124,12 @@ class PropagatingModes:
     Notes
     =====
     The sort order of all the three arrays is identical. The first half of the
-    modes have negative velocity, the second half have positive velocity. The
-    modes with negative velocity are ordered from larger to lower momenta, the
-    modes with positive velocity vice versa.
+    modes have negative velocity, the second half have positive velocity.
+    Within these halves the modes are ordered by the eigenvalues of any
+    declared conservation laws. Within blocks with the same conservation law
+    eigenvalue the modes with negative velocity are ordered by increasing
+    momentum, and the modes with positive velocity are ordered by decreasing
+    momentum. Finally, modes are ordered by the magnitude of their velocity.
 
     The first dimension of `wave_functions` corresponds to the orbitals of all
     the sites in a unit cell, the second one to the number of the mode.  Each