We tested three mathematical models of associative recall that differ in the assumed structure of the memory trace (direct or indirect connections between parts) and the interdependence of the connections (independent or correlated). The three models compared are the “horizontal” model with direct, independent connections, the “schema” model with indirect, independent connections, and the “fragment” model with indirect, correlated connections. In Experiment 1, subjects studied quartets of minimally related words and then recalled, using one or two words of each quartet as cues. The horizontal and schema models predicted the data very well, but the fragment model did poorly. In Experiment 2, related word quintets were learned, and recall cues contained one, two, or three words of a quintet. Only the schema model adequately fit these data. Experiment 3 directly tested the fragment model, using sequential tests of unrelated word quartets. Even an augmented fragment model with extra recall failure parameters was decisively rejected by these data. Both the horizontal and schema models gave satisfactory qualitative accounts, although poor quantitative fits. A means of deriving the models through a spreading activation semantic network of preexperimental knowledge is suggested, and related models are discussed.