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We propose an improved abstract interpretation based method for quantifying cache side-channel leakage by addressing two key components of precision loss in existing set-based cache abstractions. Our method targets two key sources of imprecision: (1) imprecision in the abstract transfer function used to update the abstract cache state when interpreting a memory access and (2) imprecision due to the incompleteness of the set-based domain. At the center of our method are two key improvements: (1) the introduction of a new transfer function for updating the abstract cache state which carefully leverages information in the abstract state to prevent the spurious aging of memory blocks and (2) a refinement of the set-based domain based on the finite powerset construction. We show that both the new abstract transformer and the domain refinement enjoy certain enhanced precision properties. We have implemented the method and compared it against the state-of-the-art technique on a suite of benchmark programs implementing both sorting algorithms and cryptographic algorithms. The experimental results show that our method is effective in improving the precision of cache side-channel leakage quantification.