We evaluate here the performance of four models of cross‐situational word learning: two global models, which extract and retain multiple referential alternatives from each word occurrence; and two local models, which extract just a single referent from each occurrence. One of these local models, dubbed Pursuit, uses an associative learning mechanism to estimate word‐referent probability but pursues and tests the best referent‐meaning at any given time. Pursuit is found to perform as well as global models under many conditions extracted from naturalistic corpora of parent‐child interactions, even though the model maintains far less information than global models. Moreover, Pursuit is found to best capture human experimental findings from several relevant cross‐situational word‐learning experiments, including those of Yu and Smith (), the paradigm example of a finding believed to support fully global cross‐situational models. Implications and limitations of these results are discussed, most notably that the model characterizes only the earliest stages of word learning, when reliance on the co‐occurring referent world is at its greatest.