The generation of random sequences is known to be a complex, demanding and effortful task for adults. This study explores random generation performance among children in three experiments. Expt 1 illustrates 8-10-year-olds' sensitivity to response speed requirements. Expt 2 shows that 8-11-year-olds were sensitive to the number of response alternatives, while there was equivalence in output quality over two types of instructional formats. Expt 3 reveals competencies in performance among 5-7-year-olds and shows that response repetitions are partly amenable to instructional emphasis. Across comparable studies, analysis confirmed a multidimensional structure to response sets. Generally, data show the potential utility of random generation as a developmental task with substantial and multifaceted attentional requirements.