The competition between two cluster fragments (KrXe12 and Xe-13) in the evaporative process of the non-rotating mixed Lennard-Jones cluster KrXe13 has been investigated both from molecular dynamics simulations and Phase Space Theory (PST). The branching ratio between the two fragments is seen to be strongly altered by the thermodynamical changes, especially the preliminary core/surface isomerization of the Kr atom. Such a multistep melting behavior is well reproduced by PST when numerically exact radial potentials along the dissociative coordinate and anharmonic vibrational densities of states are considered. (C) 2003 Elsevier B.V. All rights reserved.