Measurements of neutral gas density in the thermosphere at the base of the Earth's south magnetic cusp from the Streak mission are reported and discussed. In contrast to recent reports of enhanced density in the cusp, these measurements show the density to be depleted relative to the surrounding region. The difference is interpreted as an altitude effect. This observation and interpretation lead to new constraints on the physical mechanisms that could explain cusp upwelling and are inconsistent with a Joule heating mechanism. A mechanism based on heating by soft cusp particle precipitation is put forth, and model calculations are used to show how it explains the relative depletions observed by Streak as well as the enhancements at higher altitudes reported previously.