Can people learn to perform two tasks at the same time without interference? To answer this question, the authors trained 6 participants for 36 sessions in a Psychological Refractory Period (PRP) experiment, where Task 1 required a speeded vocal response to an auditory stimulus and Task 2 required a speeded manual response to a visual stimulus. The large PRP effect found initially (353 ms in Session 1) shrank to only about 40 ms over the course of practice, disappearing entirely for 1 of the 6 participants. This reduction in the PRP effect with practice is considerably larger than has been previously reported. The obtained pattern of factor interactions between stimulus onset asynchrony and each of three task difficulty manipulations (Task 1 judgment difficulty, Task 2 stimulus contrast, and Task 2 mapping compatibility) supports a postponement (bottleneck) account of dual-task interference, both before and after practice.