This study systematically examined developmental changes in the flexibility of preschool children's counting skills by assessing their use of counting to solve different kinds of quantitative problems at several preschool age levels. Three principal kinds of quantitative problems were considered: (1) quantifying a given set; (2) generating a set of a specified numerosity; and (3) comparing two numerical quantities. In the first experiment 18 three-year-olds and 18 three-and-one-half-year-olds were tested on a relative numerosity task and on counting sets of objects. The second experiment included 17 three-and-one-half-year-olds, 19 four-year-olds, and 18 four-and-one-half-year-olds; they were tested on numerosity and on counting a wider variety of quantitative problems. Recurrent limitations on young children's use of counting were found that cannot be wholly explained either by lack of knowledge about how to count or by performance factors. Young children's limited use of counting may stem from important restrictions on what they understand about when or why they should count. Educational implications are then discussed. (MNS)