Molded plastic barrier segments, typically water or sand-ballasted, are engineered to be attached together, end-to-end, in a barrier array, with innovative features which result in low rotation between attached barrier segments. Such a low rotation barrier array will, upon impact by a vehicle, act as a re-directive barrier, rather than a capturing barrier, which is an important safety feature in some crash scenarios, particularly with respect to more recent safety specifications required by many governmental highway agencies.