Summary Although many types of newly encoded information can be consolidated during sleep, an enhanced effect has been found for memories tagged as relevant to the future, such as through knowledge of future testing or payment for successful recall. In the current study, participants (n = 80) learned Welsh and Breton translations of English words, and intrinsic relevance of learned material was operationalized as perceived value of the Welsh and Breton languages. Participants were non‐Welsh native English speakers who had recently arrived in Wales. Memory for the words was tested immediately and 12 h later, after either a period of wake or a period of sleep. An increase in recall for both languages was found after sleep, but not after wake. Importantly, for the sleep condition, overnight improvement in Welsh word recall was associated with participants’ level of valuing the Welsh language. This association was not found for the wake period condition. These findings support previous indications of an active role of sleep in the consolidation of memories relevant for the future, and demonstrate that this effect may be modulated by individual differences in perceived value of the learned material. It remains to be established whether this association is mediated by an emotional attachment to the language or a cognitive facility with it, or both.