Though there is substantial evidence that individuals can prioritize more valuable information in visual working memory (WM), little research has examined this in the verbal domain. Four experiments were conducted to investigate this and the conditions under which effects emerge. In each experiment, participants listened to digit sequences and then attempted to recall them in the correct order. At the start of each block, participants were either told that all items were of equal value, or that an item at a particular serial position was worth more points. Recall was enhanced for these higher value items (Experiment 1a), a finding that was replicated while rejecting an alternative account based on distinctiveness (Experiment 1b). Thus, valuable information can be prioritized in verbal WM. Two further experiments investigated whether these boosts remained when participants completed a simple concurrent task disrupting verbal rehearsal (Experiment 2), or a complex concurrent task disrupting verbal rehearsal and executive resources (Experiment 3). Under simple concurrent task conditions, prioritization boosts were observed, but with increased costs to the less valuable items. Prioritization effects were also observed under complex concurrent task conditions, although this was accompanied by chance-level performance at most of the less valuable positions. A substantial recency advantage was also observed for the final item in each sequence, across all conditions. Taken together, this indicates that individuals can prioritize valuable information in verbal WM even when rehearsal and executive resources are disrupted, though they do so by neglecting or abandoning other items in the sequence.