Rapid execution of motor sequences is believed to depend on fusing movement elements into cohesive units that are executed holistically. We sought to determine the contribution of primary motor and dorsal premotor cortex to this ability. Monkeys performed highly practiced two-reach sequences, interleaved with matched reaches performed alone or separated by a delay. We partitioned neural population activity into components pertaining to preparation, initiation and execution. The hypothesis that movement elements fuse makes specific predictions regarding all three forms of activity. We observed none of these predicted effects. Rapid two-reach sequences involved the same set of neural events as individual reaches but with preparation for the second reach occurring as the first was in flight. Thus, at the level of dorsal premotor and primary motor cortex, skillfully executing a rapid sequence depends not on fusing elements, but on the ability to perform two key processes at the same time.