For a special class of tests a model is presented which, as a distinguishing feature, assumes closure of the set of all item characteristic functions under multiplication and a certain exponentiation. It is shown that essentially unique parallelization of the set of corresponding trace lines is attainable if and only if all item characteristic functions are powers of each other. The required continuous and monotone transformation of the ability continuum is explicitly given. Upon transformation all item characteristic functions assume a unique functional form regardless of their initial form. The model rules out normal ogives as well as logistic functions as possible item characteristic functions after transformation.