Researchers have argued that traditional elicited-response false-belief tasks involve considerable processing demands and hence underestimate children's false-belief understanding. Consistent with this claim, Setoh et al. (2016) recently found that when processing demands were sufficiently reduced, children could succeed in an elicited-response task as early as 2.5 years of age. Here we examined whether 2.5-year-olds could also succeed in a low-demand elicited-response task involving false beliefs about identity, which have been argued to provide a critical test of whether children truly represent beliefs, while also clarifying how the practice trials in Setoh et al.'s task facilitated children's elicited-response performance. 2.5-year-olds were tested in a version of Setoh et al.'s elicited-response task in which they heard a location or identity false-belief story. We varied whether the practice trials had the same type of wh-question as the test trial. Children who heard the same type of wh-question on all trials succeeded regardless of which story they heard (location or identity) and performance did not differ across belief type. This replicates Setoh et al.'s positive results and demonstrates that when processing demands are sufficiently reduced, children can succeed in elicited-response tasks involving false beliefs about object location or identity. This suggests that children are capable of attributing genuine false beliefs prior to 4 years of age. However, children performed at chance if the practice trials involved a different type of wh-question than the test trials, suggesting that at this age practice with the wh-question used in the test trial is essential to children's success.