Geologic evidence suggests that in the Late Neoproterozoic (~600 Ma) almost all land masses were glaciated, with sea-level glaciation existing even at the equator. A recent modeling study has shown that it is possible to simulate an ice-covered Earth glaciation with a coupled climate/ice-sheet model. However, separate general circulation model experiments suggest that a second solution may exist with a substantial area of ice free ocean in the tropics. Although 0.1 to 0.3 of an atmosphere of CO2 (~300 to 1000 X) is required for deglaciation of a Snowball Earth, the exit CO2 levels for an open water solution could be significantly less. In this paper we utilize a coupled climate/ice sheet model to demonstrate four points: (1) the open water solution can be simulated in the coupled model if the sea ice parameter is adjusted slightly; (2) a major reduction in ice volume from the open water/equatorial ice solution occurs at a CO2 level of about 4X present values-about two orders of magnitude less than required for exit from the hard snowball initial state; (3) additional CO2 increases are required to get fuller meltback of the ice; and (4) the open water solution exhibits hysteresis properties, such that climates with the same level of CO2 may evolve into either the snowball, open water, or a warmer world solution, with the trajectory depending on initial conditions. These results set useful targets for geochemical calculations of CO2 changes associated with the open-water solution. ¿ 2001 American Geophysical Union