When children come to grasp the concept of intention is a central question in theory of mind research. Existing studies, however, present a puzzling picture. On the one hand, infants distinguish between intentional and accidental actions. On the other hand, previous work suggests that until 8 years of age children do not yet understand an essential property of intentions—their aspectuality. Intentions are aspectual in the sense that they refer to objects and actions only under specific aspects. For example, Oedipus married Jocasta without knowing that she was his mother. Thus, he intentionally married Jocasta but did not intentionally marry his mother. However, the negative findings from these studies may indicate performance limitations rather than competence limitations. The rationale of the current set of studies, therefore, was to test children’s understanding of the aspectuality of intentions in a simplified, cognitively less demanding design. The participants, 5- and 6-year-olds (Study 1) and 4-year-olds (Study 2), were involved in simple games where they (or another agent) intentionally acted on objects that had an obvious first identity and a hidden second identity. Children either did or did not know about the toy’s second identity at the moment of acting. After their actions, children were asked about their intentions regarding the toys’ different identities. Results revealed that the 5- and 6-year-olds, but not the 4-year-olds, systematically considered how they (or another agent) represented the objects when making intentionality judgments. Thus, an understanding of aspectual intentions seems to develop at around the late preschool years—much earlier than previously assumed.