Loftus and his colleagues have proposed an Independent Sampling model to account for performance in a number of whole report tasks. The Independent Sampling model states that items in the display are acquired independently; for example, the probability of acquiring item one of a four item display does not depend on the probability of acquiring item two. We evaluate the Independent Sampling model and three other candidate models with four statistics that examine inter-item dependencies in a character identification task. Two candidate models, the Fixed Path Poisson and Weighted Path Poisson models have a serial processing architecture and a poisson process, while the third candidate model is a variant of the Independent Sampling model with variable attention across trials. We conclude that the Independent Sampling model cannot account for the observed inter-item dependencies. Adding a variable attention component allows this model to account for the inter-item dependencies, but it does so using a mechanism that adds too much variability to the predicted responses. The Weighted Path Poisson model accounts for virtually all characteristics of the dependency and marginal data with a relatively modest number of parameters. Models based on the opposite architecture (serial to parallel or vice versa) that mimic these models are also discussed.