In many multi-core architectures, inclusive shared caches are used to reduce cache coherence complexity. However, the enforcement of the inclusion property can cause invalidation of memory blocks at higher cache levels. In order to ensure safety, analysis of cache hierarchies with inclusive caches for worst-case execution time (WCET) estimation is typically based on conservative decisions. Thus, the estimation may not be tight. In order to tighten the estimation, this paper proposes an approach that can more precisely analyze the behavior of a cache hierarchy maintaining the inclusion property. We illustrate the approach in the context of multi-level instruction caches. The approach first analyzes all the inclusive caches in the hierarchy in a bottom-up direction, and then analyzes the remaining non-inclusive caches in a top-down direction. In order to capture the inclusion victims and their effects, we also propose a concept of aging barrier and integrate it with the traditional must and persistence analyses to safely slow down their aging process so as to derive more precise analyses. We evaluate the proposed approach on a set of benchmarks and the evaluation reveals that the estimations are tightened.