The combined effect of ion-neutral collisions and strong dc electric fields is known to drive marked departures from a simple Maxwellian shape in the supersonic ions of the auroral ionosphere. With the current strong interest in investigating highly disturbed periods, an accurate knowledge of the ion distribution function is gaining in importance. It is known that the shape of the ion velocity distribution below 500 km can have a pronounced toroidal character in the case of O+ ions while looking more like an ellipsoid of revolution in the NO+ case. Calculations of these effects have been made using analytical expansion techniques as well as numerical Monte Carlo simulations. While the two approaches yield results that are in qualitative agreement with each other, we show that there can at times be some important quantitative differences between the two techniques. This should not be surprising in view of the fact that analytic expansions are based on collision models that are independent of the relative energy between colliding particles, while the more recent Monte Carlo calculations do not suffer from this limitation. This drawback notwithstanding, the advantage of analytical techniques lies with the speed of the computations; these techniques are also free of the statistical noise that can clutter the Monte Carlo results. The latter can, however, be used to improve the accuracy of the analytical calculations and therefore their usefulness. This is done here by obtaining a new model of collision cross section integrals which is extracted from the more recent Monte Carlo results. For strong dc electric field conditions, the new model can, in all cases, greatly enhance the accuracy of the analytical temperature calculations. The new model also produces overall shapes that are in better agreement with the numerical simulations in the NO+ case. However, even with the new generalized cross section model, the analytical description of O+ ions remains problematic above 100 mV/m in an atmosphere with a strong atomic oxygen content. ¿ 1998 American Geophysical Union