While recent studies suggest children can use cross-situational information to learn words, these studies involved minimal referential ambiguity, and the cross-situational evidence overwhelmingly favored a single referent for each word. Here we asked whether 2-5-year-olds could identify a noun's referent when the scene and cross-situational evidence were more ambiguous. Children saw four trials in which a novel word occurred with four novel objects; only one object consistently co-occurred with the word across trials. The frequency of distracter objects varied across conditions. When all distracter referents occurred only once (no-competition), children successfully identified the noun's referent. When a high-probability competitor referent occurred on three trials, children identified the target referent if the competitor was absent on the third trial (short-competition) but not if it was present until the fourth trial (long-competition). This suggests that although 2-5-year-olds' cross-situational learning scales up to more ambiguous scenes, it is disrupted by high-probability competitor referents.