Based on curvature energy considerations, nonbilayer phase-forming phospholipids in excess water should form stable bicontinuous inverted cubic (Q(II)) phases at temperatures between the lamellar (L(alpha)) and inverted hexagonal (H(II)) phase regions. However, the phosphatidylethanolamines (PEs), which are a common class of biomembrane phospholipids, typically display direct L(alpha)/H(II) phase transitions and may form intermediate Q(II) phases only after the temperature is cycled repeatedly across the L(alpha)/H(II) phase transition temperature, T(H), or when the H(II) phases are cooled from T > T(H). This raises the question of whether models of inverted phase stability, which are based on curvature energy alone, accurately predict the relative free energy of these phases. Here we demonstrate the important role of a noncurvature energy contribution, the unbinding energy of the L(alpha) phase bilayers, g(u), that serves to stabilize the L(alpha) phase relative to the nonlamellar phases. The planar L(alpha) phase bilayers must separate for a Q(II) phase to form and it turns out that the work of their unbinding can be larger than the curvature energy reduction on formation of Q(II) phase from L(alpha) at temperatures near the L(alpha)/Q(II) transition temperature (T(Q)). Using g(u) and elastic constant values typical of unsaturated PEs, we show that g(u) is sufficient to make T(Q) > T(H) for the latter lipids. Such systems would display direct L(alpha) --> H(II) transitions, and a Q(II) phase might only form as a metastable phase upon cooling of the H(II) phase. The g(u) values for methylated PEs and PE/phosphatidylcholine mixtures are significantly smaller than those for PEs and increase T(Q) by only a few degrees, consistent with observations of these systems. This influence of g(u) also rationalizes the effect of some aqueous solutes to increase the rate of Q(II) formation during temperature cycling of lipid dispersions. Finally, the results are relevant to protocols for determining the Gaussian curvature modulus, which substantially affects the energy of intermediates in membrane fusion and fission. Recently, two such methods were proposed based on measuring T(Q) and on measuring Q(II) phase unit cell dimensions, respectively. In view of the effect of g(u) on T(Q) that we describe here, the latter method, which does not depend on the value of g(u), is preferable.