When tested with traditional false-belief tasks, which require answering a standard question about the likely behavior of an agent with a false belief, children perform below chance until age 4 y or later. When tested without such questions, however, children give evidence of false-belief understanding much earlier. Are traditional tasks difficult because they tap a more advanced form of false-belief understanding (fundamental-change view) or because they impose greater processing demands (processing-demands view)? Evidence that young children succeed at traditional false-belief tasks when processing demands are reduced would support the latter view. In prior research, reductions in inhibitory-control demands led to improvements in young children's performance, but often only to chance (instead of below-chance) levels. Here we examined whether further reductions in processing demands might lead to success. We speculated that: (i) young children could respond randomly in a traditional low-inhibition task because their limited information-processing resources are overwhelmed by the total concurrent processing demands in the task; and (ii) these demands include those from the response-generation process activated by the standard question. This analysis suggested that 2.5-y-old toddlers might succeed at a traditional low-inhibition task if response-generation demands were also reduced via practice trials. As predicted, toddlers performed above chance following two response-generation practice trials; toddlers failed when these trials either were rendered less effective or were used in a high-inhibition task. These results support the processing-demands view: Even toddlers succeed at a traditional false-belief task when overall processing demands are reduced.