Mounting evidence suggests that human motor control uses dynamic primitives, attractors of dynamic neuromechanical systems that require minimal central supervision. However, advantages for control may be offset by compromised versatility. Extending recent results showing that humans could not sustain discrete movements as duration decreased, this study tested whether smoothly rhythmic movements could be maintained as duration increased. Participants performed horizontal movements between two targets, paced by sounds with intervals that increased from 1 to 6 s by 200 ms per cycle and then decreased again. The instruction emphasized smooth rhythmic movements without interspersed dwell times. We hypothesized that ) when oscillatory motions slow down, smoothness decreases; ) slower oscillatory motions are executed as submovements or even discrete movements; and ) the transition between smooth oscillations and submovements shows hysteresis. An alternative hypothesis was that ) removing visual feedback restores smoothness, indicative of visually evoked corrections causing the irregularity. Results showed that humans could not perform slow and smooth oscillatory movements. Harmonicity decreased with longer intervals, and dwell times between cycles appeared and became prominent at slower speeds. Velocity profiles showed an increase with cycle duration of the number of overlapping submovements. There was weak evidence of hysteresis in the transition between these two types of movement. Eliminating vision had no effect, suggesting that intermittent visually evoked corrections did not underlie this phenomenon. These results show that it is hard for humans to execute smooth rhythmic motions very slowly. Instead, they "default" to another dynamic primitive and compose motion as a sequence of overlapping submovements. Complementing a large body of prior work showing advantages of composing primitives to manage the complexity of motor control, this paper uncovers a limitation due to composition of behavior from dynamic primitives: while slower execution frequently makes a task easier, there is a limit and it is hard for humans to move very slowly. We suggest that this remarkable limitation is not due to inadequacies of muscle, nor to slow neural communication, but is a consequence of how the control of movement is organized.