The domain-growth kinetics of p=fourfold degenerate (2×1) ordering in two-dimensional Ising models with conserved density is studied as a function of temperature and range of Kawasaki spin exchange. It is found by computer simulations that the zero-temperature freezing-in behavior for nearest-neighbor exchange is released when next-nearest-neighbor exchange is included. The Lifshitz-Allen-Cahn growth law is obeyed for all temperatures indicating that the density conservation is irrelevant also for p>2.. AE