All current models of visual whole report processing assume perceptual independence among the displayed items in which the perceptual processing of individual items is not affected by other items in the display. However, models proposed by Townsend (1981, Acta Psychologica 47, 149-173), Shibuya and Bundesen (1988, Journal of Experimental Psychology: Human Perception and Performance 14, 591-600), and Bundesen (1990, Psychological Review 97, 523-547) contain postperceptual buffers that must predict negative dependencies. The perceptual-independence assumption forms what we term the modal model class. A recent example of a model that assumes perceptual independence is the Independent Sampling Model of Loftus, Busey, and Senders (1993, Perception and Psychophysics 54, 535-554). The fundamental independence assumption has only been directly tested once before, where tests revealed no dependencies except those produced by guessing. The present study tests the independence assumption using several different statistics and, contrary to most extant models of whole report, finds significant positive dependence. Poisson models do predict a positive dependence and we develop a succinctly parameterized version, the Weighted Path Poisson Model, which allows the finishing order to be a weighted probabilistic mechanism. However, it does not predict the data quite as well as a new model, the Variable Attention Model, which allows independence within trials (unlike the Poisson models). This model assumes that attention (or, potentially, other aspects such as signal quality) varies widely across trials, thus predicting an overall positive dependence. Intuitions for and against the competing models are discussed. In addition, we show, through mimicking formulae, that models which contain the proper qualitative type of dependence structure can be cast in either serial or parallel form. Copyright 2001 Academic Press.