We introduce a new approach, CONCH, for de-bloating contexts for all the object-sensitive pointer analysis algorithms developed for object-oriented languages, where the calling contexts of a method are distinguished by its receiver objects. Our key insight is to approximate a recently proposed set of two necessary conditions for an object to be context-sensitive, i.e., context-dependent (whose precise verification is undecidable) with a set of three linearly verifiable conditions (in terms of the number of statements in the program) that are almost always necessary for real-world object-oriented applications, based on three key observations regarding context-dependability for their objects used. To create a practical implementation, we introduce a new IFDS-based algorithm for reasoning about object reachability in a program. By debloating contexts for two representative object-sensitive pointer analyses applied to a set of 12 representative Java programs, CONCH can speed up the two baselines together substantially (3.1x on average with a maximum of 15.9x) and analyze 7 more programs scalably, but at only a negligible loss of precision (less than 0.1%).