This research investigates the nature of similarity relations among three pairs of interacting dimensions: (1) the integral dimensions of auditory pitch and loudness, (2) the configural dimensions of paired parentheses, and (3) the cross-modally corresponding dimensions of visual position and auditory pitch. We evaluated the rules by which information from each dimension combines in similarity judgments. Our claim is that, when judging similarity, processes that are obligatory, or what we call mandatory processes, can commingle with processes of choice, or what we call optional processes. By varying instructions, we found strong evidence of optional processing. Instructions to rate overall similarity encouraged subjects to attend to stimuli as wholes and led to a Euclidean rule in similarity scaling. Instructions to focus on dimensions encouraged subjects to consider each stimulus dimension separately and led to a city-block rule. We argue that optional processes may obscure mandatory ones, and so need to be identified before mandatory processes can be understood.