Existing precise context-sensitive heap analyses do not scale well for large OO programs. Further, identifying the right context abstraction becomes quite intriguing as two of the most popular categories of context abstractions (call-site- and object-sensitive) lead to theoretically incomparable precision. In this paper,we address this problem by first doing a detailed comparative study (in terms of precision and efficiency) of the existing approaches, both with and without heap cloning. In addition, we propose novel context abstractions that lead to a new sweet-spot in the arena. We first enhance the precision of level-summarized relevant value (LSRV) contexts (a highly scalable abstraction with precision matching that of call-site-sensitivity) using heap cloning. Then, motivated by the resultant scalability, we propose the idea of mixing various context abstractions, and add the advantages of k-object-sensitive analyses to LSRV contexts, in an efficient manner. The resultant context abstraction, which we call lsrvkobjH, also leads to a novel connection between the two broad variants of otherwise incomparable context-sensitive analyses. Our evaluation shows that the newer proposals not only enhance the precision of both LSRV contexts and object-sensitive analyses (to perform control-flow analysis of Java programs), but also scale well to large programs. © 2020 Association for Computing Machinery.