We have measured both proton (TH+) and oxygen ion (TO+) temperatures simultaneously from spectra obtained in the lower topside ionosphere using the Arecibo incoherent scatter radar (ISR). This is the first time that two ion temperatures and three ion compositions have been measured from the same IS spectrum, and, as far as we know, one of the first measurements of both ion temperatures in the ionosphere. First we describe our spectral-domain analysis technique, emphasizing the ability to determine goodness of fit, which allows of the need for and effect of including a parameter to be numerically evaluated. We then show that common TH+ and TO+ allow insufficient freedom, and that separate temperatures are sufficient. A small negative bias in [He+> parameter is removed when the second temperature is allowed to be free while the H+ fraction is not significantly affected. We also show that the measurement cannot be made at altitudes where little O+ is present. The difference between TH+ and TO+ is zero (or at least very small) during the night, and rises to several hundred degrees at about 500 km shortly after sunrise. During the middle of the day the temperature difference declines (presumably due to higher densities) and then rises again before sunset. ¿ American Geophysical Union 1996