We derive a control-flow analysis that approximates the interproce- dural control-flow of both function calls and returns in the presence of first-class functions and tail-call optimization. In addition to an abstract environment, our analysis computes for each expression an abstract control stack, effectively approximating where func- tion calls return across optimized tail calls. The analysis is sys- tematically calculated by abstract interpretation of the stack-based CaEK abstract machine of Flanagan et al. using a series of Galois connections. Abstract interpretation provides a unifying setting in which we 1) prove the analysis equivalent to the composition of a continuation-passing style (CPS) transformation followed by an abstract interpretation of a stack-less CPS machine, and 2) extract an equivalent constraint-based formulation, thereby providing a ratio- nal reconstruction of a constraint-based control-flow analysis from abstract interpretation principles.