Using two Monte Carlo models, we have calculated the ejection of O atoms from an atomic oxygen thermosphere which is bombarded by energetic O+. In these calculations, incident oxygen ions strike atmospheric O, heating the atmosphere and setting O atoms on escape trajectories. For those ion fluxes most relevant to atmospheric sputtering at Mars, the full Monte Carlo model (DSMC model) is found to give the same sputtering yield as the Monte Carlo model in which the atmospheric structure is ignored and only the energetic atoms are tracked. In both models the sputtering yield is reduced by the electronic energy loss by the ions. The yield depends weakly on the details of the interaction potential if the relative amounts of forwardscattering to backscattering are realistic. The ejected atom energy spectra for the mean incident angle 55¿ are shown to be harder than the standard collision cascade distribution, close to the so-called incomplete cascade distribution. Yields for grazing incidence and for a thin atmosphere such as Europa's are given, and the analytic models used earlier are tested. Because the isotope ratios at Mars are likely to have been determined by atmospheric sputtering, Ar and Ne are included as constituents to verify the analytic models for the sputtering of trace species. The yields calculated here for an atomic O thermosphere can be used to estimate the sputtering of an atmosphere having molecules at the exobase. For Mars, ignoring feedback processes and using the ion fluxes listed by Johnson and Luhmann <1998>, the loss is ~0.45 bar, of which ~0.15 bar is CO2 with the largest uncertainty for atmospheric loss being the incident ion flux. ¿ 2000 American Geophysical Union