A melt encasement (fluxing) technique has been used to systematically study the velocity-undercooling relationship in samples of Cu and Cu-O and Cu-3 wt% Sn at undercoolings up to 250 K. In pure Cu the solidification velocity increased smoothly with undercooling up to a maximum of 97 m s(-1). No evidence of grain refinement was found in any of the as-solidified samples. However, in Cu doped with > 200 ppm O we found that samples undercooled by more than 190 K had a grain refined microstructure and that this corresponded with a clear discontinuity in the velocity-undercooling curve. Microstructural evidence in these samples is indicative of dendritic fragmentation having occurred. In Cu-Sn grain refinement was observed at the highest undercoolings (greater than 190 K in Cu-3 wt% Sn) but without the spherical substructure seen to accompany grain refinement in Cu-O alloys. Microstructural analysis using light microscopy, texture analysis and microhardness measurements reveals that recrystallisation accompanies the grain refinement at high undercoolings. Furthermore, at undercoolings between 110 K and 190 K, a high density of subgrains are seen within the microstructure which indicate the occurrence of recovery, a phenomenon previously unreported in samples solidified from highly undercooled melts.