Three experiments investigated changes from 15 to 30 months of age in children's (N = 114) mastery of relations between an object and an aperture, supporting surface, or form. When choosing between objects to insert into an aperture, older children selected objects of an appropriate size and shape, but younger children showed little selectivity. Further experiments probed the sources of younger children's difficulty by comparing children's performance placing a target object in a hole, on a 2-dimensional form, or atop another solid object. Together, the findings suggest that some factors limiting adults' object representations, including the difficulty of comparing the shapes of positive and negative spaces and of representing shapes in 3 dimensions, contribute to young children's errors in manipulating objects.