The efficiency at maximum power (EMP) is investigated for classical irreversible thermal or chemical model engines. The heat or particle transport is governed by flux-force relations of the general power-law type. Special attention is given to engines that feature asymmetric transport laws, one for input (of heat or particles) and a different one for output. It is shown that in a couple of case studies, the EMP of such engines is close to the lowest of the two EMPs that would result for symmetric implementations of the transport laws. As a consequence, ideal efficiency at maximum power is only possible in the model in which both flux-force relations are of step-function type.