Speakers often use ambiguous referential utterances to inform listeners about specific referents. The four experiments examined constraints on children’s understanding of the speaker’s meaning in using such utterances concerning evaluation of knowledge sufficiency, access to common ground information in memory, and response decision processes for dealing with insufficiency. Kindergarten, second-grade, and fourth-grade children listened to short vignettes containing a referential utterance that was ambiguous or informative about the intended referent in a display. For the ambiguous utterances, the context variably contained information useful for the identification of the referent. After each vignette, the children were asked about knowledge sufficiency and asked to pick the referent or respond “don’t know.” The format of the contextual information was varied in each experiment as a way of determining problems of memory access, and Experiments 2, 3, and 4 contained direct manipulations of memory variables. Experiment 1 addressed children’s response decision processes. The results provided systematic information about the role of memory variables and response decisions processes in interpreting ambiguous referential utterances, established the importance of distinguishing between evaluation and regulation processes in children’s monitoring of referential ambiguity, and established surprising competence in 5-year olds in evaluating knowledge sufficiency. © 1993 Academic Press, Inc.