Points-to analysis for Java benefits greatly from context sensitivity. CFL-reachability and k-limited context strings are two approaches to obtaining context sensitivity with different advantages: CFL-reachability allows local reasoning about data-value flow and thus is suitable for demand-driven analyses, whereas k-limited analyses allow object sensitivity which is a superior calling context abstraction for object-oriented languages. We combine the advantages of both approaches to obtain a context-sensitive analysis that is as precise as k-limited context strings, but is more efficient to compute. Our key insight is based on a novel abstraction of contexts adapted from CFL-reachability that represents a relation between two calling contexts as a composition of transformations over contexts.