According to a traditional assumption about working memory, participants retain a series of verbal items for immediate recall using covert verbal rehearsal, without much need for attention. We reassessed this assumption by imposing a speeded, nonverbal choice reaction time (CRT) task following the presentation of each digit in a list to be recalled. When the memory load surpassed a few items, performance on the speeded CRT task became increasingly impaired. This CRT task impairment depended only on attention-related components of working memory; it was not alleviated by the presence of an auditory memory trace that automatically helped the recall of items at the ends of spoken lists. We suggest that attention-demanding refreshing of verbal stimuli occurs along with any covert rehearsal.