We implemented a new approach to measuring the relative speeds of different cognitive processes, one that extends multinomial models of memory and reasoning from discrete decisions to latencies. We applied it to the dual-process prediction that familiarity is faster than recollection. Relative to prior work on this prediction, the advantages of the new approach are that it jointly measures specific retrieval processes and their latencies, provides separate sets of latency-retrieval parameters for list items and related distractors, and supplies latency parameters for bias processes as well as retrieval processes. Six experiments were conducted using a design (conjoint recognition) in which subjects make traditional old/new decisions about probes, plus two other types of decisions (New but similar to old items? Old or new but similar to old items?). The relative speeds of context recollection, target recollection, familiarity, and bias processes were measured for old list items and for related distractors. Four patterns emerged in all experiments: (a) The speed of recollection did not differ from the speed of familiarity for list items. (b) The speed ordering was context recollection > target recollection = familiarity for related distractors. (c) Bias processes were slower than recollection and familiarity for both list items and related distractors. (d) Bias processes were faster in conditions in which list items were to be accepted than in conditions in which they were to be rejected. Overall, the results suggest that the relative speeds of different retrieval and bias processes are emergent properties of the efficiency of different retrieval cues.