In this paper, we address the larger notion of cooperation in interaction and its underlying dimensions as defined in Conversation Analysis: alignment and affiliation. Focusing on three cases from three different languages we investigate a specific practice, that of anticipatory completions, in a particular context, that of storytelling, and show that the practice of completing another speaker’s turn in an anticipatory manner is not de facto definable as either an aligning or non-aligning action, nor can it be said to be (...) either affiliating or non-affiliating. Through our analyses, we aim to distinguish and illustrate the manifold layers of and perspectives to alignment and affiliation and argue for their relevance for studies of interactional phenomena. We conclude that the notion of cooperation and its implementation through affiliating and/or aligning actions is a multi-layered and complex issue, the intricacies of which are best understood and captured through detailed sequential analyses. (shrink)