Air abrasion of zircon grains can remove metamict material that has lost radiogenic Pb and zircon overgrowths that were added during younger events and thereby improve the precision of the age measurements and permit closer estimates of the original age. Age discordance that resulted from a single disturbance of the U-Pb isotopic decay systems, as had been demonstrated by T.E. Krogh, can be considerably reduced, and, under favorable conditions, the ages brought into concordancy. Two or more events complicate the U-Pb systematics, but a series of abrasion experiments can be helpful in deciphering the geologic history and in arriving at a useful interpretation of the probable times of origin and disturbances. In east-central Minnesota, U.S.A., Penokean tonalite gneiss is dated at 1869 ?? 5 Ma, and sheared granite gneiss is shown to have been a high-level granite intrusion at 1982 ?? 5 Ma in the McGrath Gneiss precursor. Tonalite gneiss and a mafic granodiorite in the Rainy Lake area, Ontario, Canada, are dated at 2736 ?? 16 and 2682 ?? 4 Ma, respectively. The tonalitic phase of the Morton Gneiss, southwestern Minnesota, is dated at 3662 ?? 42 Ma. ?? 1986.