Previous research shows that human learners can acquire word-referent pairs over a short series of individually ambiguous situations each containing multiple words and referents (Yu & Smith, 2007). In this kind of cross-situational statistical learning based on the repeated co-occurrence of words with their intended referents, the application of principles such as mutual exclusivity and contrast can leverage prior experience to reduce the complexity in situations with multiple words and multiple referents. However, these principles can also block the learning of one-to-many mappings. In a study analogous those done in traditional associative learning, we manipulate the early and late evidence for particular pairings in the cross-situational learning paradigm, and examine the effects on learning of both one-to-one and many-to-many mappings. Two major findings are: 1) participants use mutual exclusivity and contrast to facilitate learning; and 2) given sufficient evidence, learners can adaptively disregard these principles and learn many-to-many mappings.