A context-sensitive analysis is an analysis in which program elements are interpreted with respect to the context in which they occur. For analyses on imperative languages, this often refers to considering the behavior of called procedures with respect to the calling-stack contexts that precede them. Algorithms for performing or approximating these types of analyses make up the core of interprocedural program analysis and are pervasive; having applications in program optimization, checkpointing, and model checking. This paper presents an abstraction of a popular form of context-sensitive analysis based on iteratively encapsulating the cumulative effect of a recurring piece of code. Given an analysis fitting this abstraction, a technique is presented for resolving queries of the form: Is there an occurring context, subject to a given stack-context constraint, in which a particular set of facts holds at a particular location? This practical technique, based on manipulating regular languages, is capable not only of answering queries of this form, but also of generating a compact mechanism for dynamically applying the output of the analysis to contexts as they occur. A comprehensive example is presented along with performance data on a case study code. Finally, a selection of potential applications is discussed.