The Lifshitz-Slyozov-Wagner (LSW) mechanism for coarsening of a binary alloy depends on the diffusion of minority (B) atoms through the A-rich matrix from one precipitate to another. An alternative mechanism is the coagulation of large precipitates. We describe computer experiments and theoretical estimates showing that if the diffusion mechanism is the exchange of neighboring atoms (Kawasaki dynamics) the LSW process always predominates, giving R proportional to t(1/3) for the time dependence of the mean precipitate radius. But if the diffusion mechanism is the exchange of an atom with a vacancy then coagulation (R proportional to t(1/5)). can predominate at intermediate times if the temperature is low enough.