We test the predictions of different computational models of cross-situational word learning that have been proposed in the literature by comparing their behavior to that of young children and adults in the word learning task conducted by Ramscar, Dye, and Klein (2013). Our experimental results show that a Hebbian learner and a model that relies on hypothesis testing fail to account for the behavioral data obtained from both populations. Ruling out such accounts might help reducing the search space and better focus on the most relevant aspects of the problem, in order to disentangle the mechanisms used during language acquisition to map words and referents in a highly noisy environment.