Let L → H be a lattice homomorphism and let a "readable" drawing of H be given. It is natural to make use of it to try getting a clear(er) drawing of L. Hence, the following question is explored: How the knowledge of the congruence lattice Con(L) of L can help in getting "better" drawings of L? This will be done by proposing rank shelling procedures of (M(Con(L),≤) and will be illustrated with examples coming either from math. or social sciences.