C. Leovy (personal communication, 2007) speculated that two stable climate states on early Mars could have resulted from interactions between the dust and CO2 cycles. In one state, a highly active dust cycle would prevent atmospheric collapse, and in the second, the collapsed atmosphere would not maintain an active dust cycle. An initial assessment of this idea is presented based on a Mars general circulation model parameter study. A range of global dust loadings, CO2 ice albedos, and obliquities are investigated to explore conditions in which increasing the atmospheric dust content stabilizes an otherwise unstable atmosphere. We find that dust only stabilizes the atmosphere at high obliquity and when the CO2 ice albedo is high. Although results suggest that two stable states could have existed on early Mars under limited conditions, further work is needed to know if the conditions necessary are physically plausible.