Theory-of-mind concepts in children with deafness, autism, and normal development (N = 154) were examined in three experiments using a set of standard inferential false-belief tasks and matched sets of tasks involving false drawings. Results of all three experiments replicated previously published findings by showing that primary school children with deafness or autism, aged 6 to 13 years, scored significantly lower than normal-developing 4-year-old preschoolers on standard misleading-container and unseen-change tests of false-belief understanding. Furthermore, deaf and autistic children generally scored higher on drawing-based tests than on corresponding standard tests and, on the most challenging of the false-drawing tests in Experiment 2, they significantly outperformed the normal-developing preschoolers by clearly understanding their own false intentions and another person's false beliefs about an actively misleading drawing. In Experiment 3, preschoolers outperformed older deaf and autistic children on standard tasks, but did less well on a task that required the drawing of a false belief. Methodological factors could not fully explain the findings, but early social and conversational experiences in the family were deemed likely contributors.