Children can use the statistical regularities of their environment to learn word meanings, a mechanism known as cross-situational learning. We take a computational approach to investigate how the information present during each observation in a cross-situational framework can affect the overall acquisition of word meanings. We do so by formulating various in-the-moment learning mechanisms that are sensitive to different statistics of the environment, such as counts and conditional probabilities. Each mechanism introduces a unique source of competition or mutual exclusivity bias to the model; the mechanism that maximally uses the model's knowledge of word meanings performs the best. Moreover, the gap between this mechanism and others is amplified in more challenging learning scenarios, such as learning from few examples.