Monte Carlo Simulations are used to investigate the recent scanning tunneling microscopy (STM) measurements of fast decaying adatom islands on Cu(111). First, reduced potential barriers for adatom migration along close-packed (01 (1) over bar} step edges having {100} or {111} step risers are shown to be very important to obtain close-to-monotonic decay of the island top layer, in correspondence to STM measurements. The best correspondence is obtained for fully suppressed one-dimensional Ehrlich-Schwoebel barriers. Second. for encounters between steps in adjacent atomic layers it is demonstrated that a moderately reduced step-edge potential energy barrier for adatom crossing of these Steps is Sufficient to obtain correspondence between simulations and experiments provided that the step-edge diffusion is increased. The step-step-interaction-related activation energy for step-edge crossing is found to be significantly lower than what was previously reported. This work shows that concerted atomic motion is not necessary to explain the rapid top-island decay if the low-coordinated step-edge transition states are properly modeled. Moreover, no critical step-step distance larger than one atomic row. for which rapid top-island decay occurs, is obtained in the simulations. Furthermore, the simulations are interesting because they show that dramatic macroscopic effects can be generated by just small changes of the potential-energy barriers that are controlling the surface diffusion rates.