We present a new technique for directly dating, by conventional techniques, the rims of zircons. Several circumstances, such as a xenocrystic or inherited component in igneous zircon and metamorphic overgrowths on igneous cores, can result in grains with physically distinct age components. Pneumatic abrasion has been previously shown by Krogh to remove overgrowths and damaged areas of zircon, leaving more resistant and isotopically less disturbed parts available for analysis. A new abrader design, which is capable of very gently grinding only tips and interfacial edges of even needle-like grains, permits easy collection of abraded material for dating. Five examples demonstrate the utility of the "dust-collecting" technique, including two studies that compare conventional, ion microprobe and abrader data. Common Pb may be strongly concentrated in the outermost zones of many zircons and this Pb is not easily removed by leaching (even in weak HF). Thus, the benefit of removing only the outermost zones (and avoiding mixing of age components) is somewhat compromised by the much higher common Pb contents which result in less precise age determinations. A very brief abrasion to remove the high common Pb zones prior to collection of material for dating is selected. ?? 1990.