Flexibility in conceptual projection constitutes one of the most challenging issues in the embodiment and conceptual metaphor literatures. We sketch a theoretical proposal that places the burden of the explanation on attentional dynamics in interaction with mental models in working memory that are constrained to be maximally coherent. A test of this theory is provided in the context of the conceptual projection of time onto the domain of space. Participants categorized words presented at different spatial locations (back–front, left–right) as referring (...) to the past or to the future. Responses were faster when the irrelevant word location was congruent with the back–past, front–future metaphoric mapping. Moreover, when a new highly task-relevant spatial frame of reference was introduced, it changed the projection of past and future onto space in a way that was congruent with the new frame (past was now projected to left space and future to right space), as predicted by the theory. This study shows that there is substantial flexibility in conceptual projection and opens a venue to study metaphoric variation across tasks, individuals, and cultures as the result of attentional dynamics. (shrink)