  Stacked directed animals and multi-directed animals are two lattice models
defined by Bousquet-M\'{e}lou and Rechnitzer in 2002. The original definitions
of those models involve heaps of pieces, i.e., some geometric representation of
partially commutative monoids. The object of this writing is to define stacked
directed animals and multi-directed animals in such a way that heaps of pieces
are not involved. Our alternative definitions are equivalent to
Bousquet-M\'{e}lou and Rechnitzer's original ones.
