To explicate the mechanisms which support attempts at random number production, two experiments explore the role of memory systems in random sequencing. In the first, subjects produced written random number sequences with two response vocabularies, and subjects were also required to estimate how often they had chosen particular values in their response set. Memory for responses was found to correlate with the quality of random generation, and sequences were less random with a larger response repertoire. However, memory performance did not account for the effect of response set size, suggesting different aetiologies for these effects. In a second experiment, subjects were given a concurrent memory load during random generation, and a concurrent task requiring avoidance of certain response values. Performance declined under dual-task conditions, and the avoidance requirement particularly impaired subjects' ability to inhibit prepotent responses. Findings are integrated into a view of random generation as a complex task with multiple performance constraints.