In theory of mind research, there is a long standing dispute about whether children come to understand the subjectivity of both desires and beliefs at the same time (around age 4), or whether there is an asymmetry such that desires are understood earlier. To address this issue, 3-year olds' understanding of situations in which two persons have mutually incompatible desires was tested in two studies. Results revealed that (i) children were quite proficient at ascribing incompatible desires to two persons, and in simpler scenarios even incompatible desire-dependent emotions; (ii) children showed this proficiency even though they mostly failed the false belief task. Overall, these results suggest that there is an asymmetry such that young children come to understand the subjective nature of desires before they understand the corresponding subjectivity of beliefs. Possible explanations for this asymmetry are discussed in light of conceptual change and information-processing accounts of theory of mind development.