Most words are associated with multiple senses. A DVD can be round (when describing a disc), and a DVD can be an hour long (when describing a movie), and in each case DVD means something different. The possible senses of a word are often predictable, and also constrained, as words cannot take just any meaning: for example, although a movie can be an hour long, it cannot sensibly be described as round (unlike a DVD). Learning the scope and limits of word meaning is vital for the comprehension of natural language, but poses a potentially difficult learnability problem for children. By testing what senses children are willing to assign to a variety of words, we demonstrate that, in comprehension, the problem is solved using a productive learning strategy. Children are perfectly capable of assigning different senses to a word; indeed they are essentially adult-like at assigning licensed meanings. But difficulties arise in determining which senses are assignable: children systematically overestimate the possible senses of a word, allowing meanings that adults rule unlicensed (e.g., taking "round movie" to refer to a disc). By contrast, this strategy does not extend to production, in which children use licensed, but not unlicensed, senses. Children's productive comprehension strategy suggests an early emerging facility for using context in sense resolution (a difficult task for natural language processing algorithms), but leaves an intriguing question as to the mechanisms children use to learn a restricted, adult-like set of senses. (Contains 1 table, 9 figures and 1 supplementary data.)