Introduction This paper is a companion to \Linearly Used Continuations" by the authors. There, we show how a variety of control behaviours use continuations anely, including calling/returning (procedures), raising/handling (exceptions), labelled jumping (goto statements), and process switching (coroutines). Our purpose here is to show how an ane typing discipline for the target of a cps transform can be used to prove a completeness result. Although many control constructs use continuations...