Conjoint measurement analysis (Luce & Tukey, 1964) usually starts out with an empirical weak order ~ over a set of stimuli S = A X X, where a and x are two com ponents of a stimulus s = (a,x), For example, assume s to be a stimulus light patch with luminance a and dura tion x, and ~ an order relation at least bright as established by the subject in an experiment. In order to represent the empirical ordering by a sum of numerical functions of each of the components, one has to find scale values ¢l(a) and ¢2(X) such that for all a,b E A and x,y E X Q>.(a) + Q>.(x) ~Q>.(b) + Q>.(y) iff (a.x) 2: (b,y) (1) (see. Krantz, Luce, Suppes, & Tversky, 1971, for a detailed discussion). To solve this problem, the order re lati?n has to be transformed into a set of inequalities, WhICh may be solved by one of the usual algorithms, for example, ORDMET by McClelland and Coombs (1975) or ORDMET2 by Lehner and Noma (1980). These pro grams generate a description of the complete solution space for a given system of inequalities. Ifa solution does not exist, then the programs try to find scale values representing the data approximately. Psychological research, however, is often concerned with testing structural properties of data, rather than with finding only scale values. In the context of additive con joint measurement, experimental tests have concentrated on the independence axiom and the double cancellation axiom, pointed out by Roberts (1979, p. 221). Com puter programs for checking these axioms have been pub l~shed by Holt and Wallsten (1975), Person (1977), Ull nch, Cummins, and Walkenbach (1978), and others. Unfortunately, independence and double cancellation are not sufficient for an additive representation to exist. Higher order cancellation axioms have to be added (Scott, 1964), but these imply an infinite number of conditions to be checked and thus they are not directly testable. Although seldom violated in small designs, shown in a simulation study by McClelland (1977) using up to 4 x 4 matrices, they become more important in larger de signs. Even if finding numerical scale values is not the main concern in an experiment, a scale construction rou tine might be necessary to provide an indirect test for the