We performed Monte Carlo simulations using a minimal lattice model with short-range interactions modeled using Flory-Huggins interactions parameters, π, to investigate morphology of ion-containing A-B diblock copolymers. A fraction of the segments in the A block, p, were ionic (labeled S) while the B block segments were nonionic (p was held fixed at 0.588). The dielectric constants of the polymers is assumed to be low, and thus charge dissociation effects are negligible. The magnitude of the π between ion and nonionic species, determined in previous experiments on poly(styrenesulfonate)-b- poly(methyl butylene), PSS-PMB, is an order of magnitude larger than that between the nonionic segments. Simulations indicate that complex morphologies such as gyroid and perforated lamellae are obtained in symmetric block copolymers wherein the volume fraction of the B block, φB, is about 0.5, while simple unperforated lamellae are obtained in asymmetric block copolymers wherein φBis about 0.25. This result is very different from the well-established phase behavior of nonionic block copolymers but consistent with experimental results of Wang et al. [Macromolecules 2010, 43, 5306]. We also make a number of additional predictions, still awaiting an experimental verification, such as the emergence of the hexagonal phase in the weak segregation limit, and a remarkable insensitivity of the product p2πN (N is the total number of segments in a copolymer chain) at the order-disorder transition to φB. © 2014 American Chemical Society.