We have investigated the kinetics of domain growth in the Ising model of a two-dimensional alloy comprising two kinds of atom plus a single vacancy, where the atoms are allowed to move only by changing places with the vacancy. Not only is this model more realistic than the more usual Kawasaki dynamics in describing the decomposition process in real metal alloys, but it can also be up to 30 times faster in terms of computing time. The domains have shapes similar to those observed in the analogous model with Kawasaki dynamics, but the asymptotic regime of domain size growth (R t1/3) is approached much faster particularly in the case of 1:1 alloy composition at low temperatures. The data also show that interface diffusion cannot fully explain the slow approach towards the asymptotic regime in the case of Kawasaki dynamics. © 1994 The American Physical Society.