This paper introduces six ways for handling a
chain of lexicographic ordering (lex-chain)
constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a
constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a
constraint and a
constraint. Experiments on academic two and three dimensional placement problems as well as on industrial problems show the benefit of such a strong integration of symmetry breaking constraints and non-overlapping ones.