Geomorphic evidence that Mars was warm enough to support flowing water about 3.8 billion years ago presents a continuing enigma that cannot be explained by conventional greenhouse warming mechanisms. Model calculations show that the surface of early Mars could have been warmed through a scattering variant of the greenhouse effect, resulting from the ability of the carbon dioxide ice clouds to reflect the outgoing thermal radiation back to the surface, This process could also explain how Earth avoided an early irreversible glaciation and could extend the size of the habitable zone on extrasolar planets around stars.