Tracking word-object co-occurrence statistics can reduce referential uncertainty during word learning. But human learners are constrained by limits on attention and memory, and therefore must store a subset of the information available---how do they select what information to store? We hypothesize that the presence of referential cues like eye gaze guides how learners allocate their attention. In three large-scale experiments with adults, we test how the presence of referential cues affects cross-situational word learning. Referential cues shift learners away from multiple hypothesis tracking towards storing only a single hypothesis (Experiments 1 and 2). In addition, learners are sensitive to the reliability of a referential cue and when it is less reliable, they are less likely to use the cue and more likely to store multiple hypotheses (Experiment 3). Together, the data suggest a rational tradeoff: In conditions of greater uncertainty, learners tend to store a broader range of information.