This paper presents a row-column (RC) association model in which the estimated row and column scores are forced to be in agreement with a priori specified ordering. Two efficient algorithms for finding the order-restricted maximum likelihood (ML) estimates are proposed and their reliability under different degrees of association is investigated by a simulation study. We propose testing order-restricted RC models using a parametric bootstrap procedure, which turns out to yield reliable "p" values, except for situations in which the association between the two variables is very weak. The use of order-restricted RC models is illustrated by means of an empirical example.