Aqueous mixtures of long-tailed lipids (e.g., dimyristoyl-phosphatidylcholine - DMPC) and detergents can sometimes form membrane disks called bicelles. Bicelles have found applications as an embedding medium for membrane proteins in the context of NMR studies and protein crystallization. However, the parameters that determine the thermodynamic stability of bicelles are not well understood. Here we report a coarse-grained simulation study of the relationship between lipid-aggregate morphology and the composition and temperature of the surfactant mixture. In agreement with experiments, we find that bicellar mixtures are destabilized at higher temperatures and detergents are present at membrane edges as well as in flat membranes with a strong preference for the edges. In addition, our results suggest that the free-energy difference between bicelles and the perforated lamellar phase is typically very small for molecules without intrinsic curvature and charge. Cone shaped surfactant molecules tend to favor the formation of bicelles; however, none of the systems that we have studied provide unambiguous evidence for the existence of thermodynamically stable bicelles in mixtures of uncharged lipids with long and short tails. We speculate that small changes in the properties of the system (charge, dopants) may make bicelles thermodynamically stable.