The effect of glancing-angle ion energy E (0.5-3.0 keV), dose D (0.3-10 X 10(16) ions cm(-2)), flux J (0.6-5.9 X 10(13) ions cm(-2) s(-1)), impingement angle phi,(6 degrees-30 degrees), and substrate temperature T-s (440-650 degrees C) on the surface morphology and crystallinity of clean and air-exposed GaAs(001) surfaces was studied. For air-exposed GaAs, the lowest roughness measured by atomic force microscopy was 0.3 nm at D = 2.3 X 10(16) ions/cm(2), E = 1 keV, and phi = 15 degrees for T-s = 570 degrees C and an approximate to 1.5X10(-5) Torr As-4 overpressure. These conditions provided sufficient sputtering to remove surface contamination, as indicated by streaky, 2 X 4 reconstructed reflection high-energy electron diffraction patterns acid C- and O-free low-energy ion scattering spectra, while avoiding ion damage as judged by cross-sectional transmission electron microscopy. Defect-free epitaxial GaAs layers were grown on the sputter-cleaned substrates. Ion bombardment of clean surfaces showed roughening at larger phi values, but smooth surfaces were maintained for phi=6 degrees. Cross-sectional transmission electron microscopy studies of clean bombarded surfaces showed that ion damage decreased with decreasing D, E, and phi, and no damage was observed over a range of conditions. Sputter yields as a function of energy and phi are reported.