The microstructures of alloys created via Additive Manufacturing (AM) can vary substantially from those present in cast or wrought products, due to the very rapid solidification associated with AM. While numerous studies have investigated the process-microstructure relationship of alloys created by Selective Laser Melting (SLM), few have investigated the effects of laser rescanning to alter the microstructure or take advantage of the rapid solidification conditions the process provides. This study investigates the effect of single- or multiple pass laser scanning upon the grain structure of Addalloy (TM), a new Al-Mg-Zr alloy strengthened via L1(2)Al(3)Zr precipitates. The bottom of the melt pools consisted of fine equiaxed grains (1.3 mu m) that nucleated from primary Al3Zr (100-400 nm) precipitates. The top of the melt pool consists of columnar grains (up to 40 mu m long), consistent with lack of Al3Zr nucleants due to Zr solute trapping from increased solidification velocities. Additional laser scanning (a second or third scan) reduces the amounts of columnar grains and increased the number equiaxed grains. The change is attributed to a shallower melt pool remelting the columnar grain region upon rescanning, due to reduced laser energy absorption and increased heat losses in the solid.