Although most ABA triblock copolymers are molecularly symmetric (i.e., the terminal blocks possess the same mass), molecularly asymmetric A1BA2 triblock copolymers are of greater fundamental interest in that they can be used to explore the transition from diblock to triblock copolymer in systematic fashion. In this study, we use a lattice Monte Carlo method known as the cooperative motion algorithm to simulate molten ABA triblock copolymers possessing a short terminal block to explore the effect of molecular asymmetry on the copolymer orderdisorder transition (ODT). Reduced ODT temperatures, discerned by simultaneously analyzing several features of the simulation results, are found to compare favorably with experimental data. Of particular interest here is the initial depression in the ODT temperature for A1BA2 copolymers possessing a relatively short terminal (A2) block. This signature feature is successfully captured by the simulations and is found to be strongly dependent on composition, but weakly dependent on copolymer chain length. (C) 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013