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The hard snowball Earth bifurcation point is determined by the level of atmospheric carbon dioxide concentration (pCO(2)) below which complete glaciation of the planet would occur. In previous studies, the bifurcation point was determined based on the assumption that the extent of continental glaciation could be neglected and the results thereby obtained suggested that very low values of pCO(2) would be required (similar to 100 ppmv). Here, we deduce the upper bound on the bifurcation point using the coupled atmosphere-ocean climate model of the NCAR that is referred to as the Community Climate System Model version 3 by assuming that the continents are fully covered by ice sheets prior to executing the transition into the hard snowball state. The thickness of the ice sheet is assumed to be that obtained by an ice-sheet model coupled to an energy balance model for a soft snowball Earth. We find that the hard snowball Earth bifurcation point is in the ranges of 600-630 and 300-320 ppmv for the 720 and 570 Ma continental configurations, respectively. These critical points are between 10 and 3 times higher than their respective values when ice sheets are completely neglected. We also find that when the ice sheets are thinner than those assumed above, the climate is colder and the bifurcation point is larger. The key process that causes the excess cooling when continental ice sheets are thin is shown to be associated with the fact that atmospheric heat transport from the adjacent oceans to the ice sheet-covered continents is enhanced in such conditions. Feedbacks from sea-ice expansion and reduced water vapor concentration further cool the oceanic regions strongly.