Many mixtures of phospholipids and cholesterol form immiscible liquid phases in a monolayer at an air-water interface. As discovered recently, some binary mixtures of phospholipid and cholesterol exhibit two upper miscibility critical points. This phenomenon can result from the reversible formation of a chemically distinct liquid product or "condensed complex" between the phospholipid and cholesterol. The present work describes an empirical connection between high melting temperatures of saturated phospholipid bilayers and the appearance of two upper miscibility critical points in cholesterol -phospholipid monolayers. A rough correlation is also found between melting temperature and the composition of the complex. Bilayer melting temperature is a convenient measure of the tendency of the phospholipid acyl chains to order, and this same tendency is evidently important for condensed complex formation.