Cost partitioning is the foundation of today’s strongest heuristics for optimal classical planning. However, computing a cost partitioning for each evaluated state is prohibitively expensive in practice. Thus, existing approaches make an approximation and compute a cost partitioning only for a set of sampled states, and then reuse the resulting heuristics for all other states evaluated during the search. In this paper, we present exact methods for cost partitioning heuristics based on linear programming that fully preserve heuristic accuracy while minimizing computational cost. Specifically, we focus on saturated post-hoc optimization and establish several sufficient conditions for when reusing a cost partitioning computed for one state preserves the estimates for other states, mainly based on a sensitivity analysis of the underlying linear program. Our experiments demonstrate that our theoretical results transfer into practice, and that our exact cost partitioning algorithms are competitive with the strongest approximations currently available, while usually requiring fewer linear program evaluations.