Bulk and thin samples of Cu 75 Ni 25 (at. pct) alloy were solidified over a range of undercoolings. Unlike the bulk samples, in which grains were significantly refined at undercoolings between 45 K and 75 K, the thin samples solidified consistently into developed dendrites till the experimentally achieved largest undercooling of 150 K. The thin samples were subsequently rapidly reheated at a rate of 300 K/s to different target temperatures between the solidus and liquidus temperature interval. Letting the target temperature of heating equal to the highest recalescence temperature in the bulk sample, grain-refined microstructures were obtained in the thin sample that initially solidified at an undercooling between 45 K and 75 K. For the other thin samples, however, the dendritic morphology was still maintained. Raising the target temperature of heating to an enough high level, grain refinement also occurred in these thin samples. It is demonstrated grains are refined only when large-scale remelting occurs in the original dendrite stems with a critical remelted fraction of about 0.82 at the stem center.