To function effectively, pulmonary surfactant must adsorb rapidly to the alveolar air/water interface, but avoid collapse from the interface when compressed to low surface tensions. Prior studies show that phospholipids in the cylindrical monolayers of the inverse hexagonal (HII) phase adsorb quickly. The monolayers have negative curvature, defined by the concave shape of the hydrophilic face. Formation of the HII structures, however, involves significant disruption of optimal chain-packing. Samples with significant spontaneous curvature, formed in the absence of applied force, may nonetheless have lamellar structures. The experiments here tested whether planar lamellar bilayers formed by phospholipids with negative spontaneous curvature might adsorb rapidly but collapse slowly. Prior studies have shown that binary mixtures of dioleoyl phosphatidylcholine-dioleoyl phosphatidylethanolamine (DOPC-DOPE) with higher mol fractions of DOPE (XPE) have more negative spontaneous curvature. Samples with higher XPE adsorbed more rapidly but also collapsed more quickly. Over that range of XPE, small angle X-ray scattering showed only lamellar structures. The HII phase was undetectable. The results suggest that the innate tendency of the phospholipids to form curved structures has primary importance for adsorption rather than the presence of HII structures. Planar structures are insufficient to minimize the tendency of spontaneous curvature to promote collapse. These findings are consistent with adsorption and collapse that occur via rate-limiting structures with significant negative curvature.