A growing body of research suggests that dual-task interference in sensory consolidation (e.g., the attentional blink, AB) and response selection (e.g., the psychological refractory period, PRP) stems from a common central bottleneck of information processing. With regard to response selection, it is well known that training reduces dual-task interference. We tested whether training that is known to be effective for response selection can also reduce dual-task interference in sensory consolidation. Over two experiments, performance on a PRP paradigm (Exp. 1) and on AB paradigms (differing in their stimuli and task demands, Exps. 1 and 2) was examined after participants had completed a relevant training regimen (T1 practice for both paradigms), an irrelevant training regimen (comparable sensorimotor training, not related to T1 for both tasks), a visual-search training regimen (Exp. 2 only), or after participants had been allocated to a no-training control group. Training that had shown to be effective for reducing dual-task interference in response selection was also found to be effective for reducing interference in sensory consolidation. In addition, we found some evidence that training benefits transferred to the sensory consolidation of untrained stimuli. Collectively, these findings show that training benefits can transfer across cognitive operations that draw on the central bottleneck in information processing. These findings have implications for theories of the AB and for the design of cognitive-training regimens that aim to produce transferable training benefits.