Previous research yielded conflicting results about when children can accurately assess their epistemic states in different hiding tasks. In Experiment 1, ninety-two 3- to 7-year-olds were either shown which object was hidden inside a box, were totally ignorant about what it could be, or were presented with two objects one of which was being put inside (partial exposure). Even 3-year-olds could assess their epistemic states in the total ignorance and the complete knowledge task. However, only children older than 5 could assess their ignorance in the partial exposure task. In Experiment 2 with one hundred and one 3- to 7-year-olds, similar results were found for children under 5 years even when more objects were shown in partial exposure tasks. Implications for children's developing theory of knowledge are discussed. (Contains 2 tables and 1 figure.)