The kinetics of small clusters of "up" spins in the two-dimensional Ising model on a square lattice is examined without the usual approximations of fixed cluster shape, constant number of "down" spins and nonsplitting-noncoagulating dynamics. New kinetic equations for the number densities of clusters of various sizes and shapes are derived and solved numerically. It is shown that the kinetic behavior of small clusters depends on their shape and that the time-dependence of the total number of down spins and the splitting and coagulation of clusters significantly affect various characteristics of the system, e.g., the range of validity of the steady-state approximation, the transient time to that state, the values of mass fluxes, etc. The influence of these factors grows with increasing temperature and supersaturation. (C) 2003 American Institute of Physics.