Four experiments explore participants' attempts to generate random sequences. Experiment 1 showed that oral random number generation is strongly affected by both response speed and response set size, in contrast to a random key-pressing task in Expt 2. Expt 3 confirmed differences between output modalities in the set size effect, and Expt 4 indicated that an important source of difficulty in producing random numbers orally lies in the requirement to represent candidate choices. Across experiments, data show a strong tendency on the part of participants to suppress response repetitions, an effect which decays over intervening responses. Whilst consistent with the possibility that random generation taps some executive functions, findings suggest the need to expand current models of attentional control in working memory to account for distinct constraints.