The advent of a multiple-channels approach to spatial vision 20 years ago raised important questions that were difficult to approach empirically, given the technology and analytic tools of the time. These questions concerned the interaction or combination of different components of a stimulus--questions that have recently resurfaced in more complex form. Classical psychophysical methods for assessing whether two stimulus aspects are coded independently (e.g., masking, adaptation, and cue-summation) provide only limited information about the nature of whatever interactions are discovered. In both older work in detection and recent work in complex pattern discrimination, we have used a double-judgment paradigm in which the observer rates two aspects of a stimulus simultaneously. The paradigm provides a rich source of information about the codes underlying each psychophysical decision and which are unique in permitting us to psychophysically investigate effects resulting from neural noise in the system. Our analyses draw on theories of dimensional interaction in signal detection theory and in information theory, and on methods from several branches of statistics, including categorical data analysis and structural equation modeling. We review the theoretical, technological, methodological, and personal influences that led us to develop this approach.