- We study the two‐dimensional (2‐D) structural and thermodynamic changes in smectic‐A/lamellar phases of self‐assembling surfactant systems, in which the rim associated with a bilayer edge has a preferred curvature. This property was not considered in previous studies of 2‐D aggregation, where an infinite bilayer emerges already at very low concentrations. A lattice Hamiltonian is used to describe the bending energy of the rim: An occupied lattice site corresponds to a minimum, disklike, micelle, and a bending energy penalty is associated with corners and straight edges depending on the value of the spontaneous curvature. When the spontaneous radius of curvature of the rim is small and the bending modulus is large, we find that the ‘‘condensation’’ transition—i.e., the ‘‘collapse’’ of the finite aggregates into a continuous bilayer—is postponed to high concentrations. At low concentrations the bending energy leads to an effective repulsive interaction between the aggregates, which in turn can result in ordered (modulated) structures for not too large ratios of thermal energy to bending energy (which is the expected situation in most systems of interest). Our model should be applicable to the systems of decylammonium chloride and cesium perflourooctanoate studied by Boden and co‐workers (NMR and conductivity measurements) and Zasadzinski and co‐workers (freeze fracture), where monodisperse micellar disks are observed to layer in stacked planes. In the latter system a 2‐D order of disk‐shaped aggregates appears within the smectic‐A layers, which is also consistent with our theory. Experimental studies of the structural evolution under further condensation of the system are not yet available.