The effect of rapid solidification upon hypereutectic Sn–Ag solder alloy has been investigated using a 6.5 m drop tube. Powder sizes ranging from > 850 to < 38 μm were produced, with equivalent cooling rates of 250 to 14,800 K s−1 for 850 and 38 μm droplets, respectively. At all cooling rates investigated, dendritic β-Sn was observed as the primary solidification phase, not proeutectic Ag3Sn as predicted by the phase diagram. The volume fraction of interdendritic eutectic was observed to decrease with increasing cooling rate, with the Ag concentration in the residual interdendritic liquid estimated at 12.5–15 wt pct Ag, far in excess of the eutectic concentration of 3.8 wt pct. Much of the Ag3Sn observed within the eutectic had a blocky, divorced eutectic appearance. A model is proposed which can explain these observations in terms of sluggish nucleation of the Ag3Sn intermetallic, coupled with a metastable phase diagram that permits significant supersaturation of Ag at modest undercooling.