Previous research has reported that children's numerical equivalence judgments are affected by surface similarity and counting ability (e.g. Mix, Huttenlocher, & Levine, 1996; Siegel, 1973), a pattern that suggests categorization processes play a role in numerical development. However, because these studies involved memory for sets, large set sizes and counting rather than labelling, the connection between numerical equivalence and non-numerical comparisons has remained tenuous. The present study sought to replicate these effects while avoiding the problems associated with previous research. Five experiments are presented in which 3-year-olds compared various sets in terms of numerical equivalence. As before, children's comparisons were significantly affected by variations in surface similarity, even when there was no memory requirement and sets were small. Also, children with strong label knowledge were more likely to recognize numerical equivalence, especially in low similarity conditions. Still, children performed better when the previous memory and set size demands were eliminated.