In behavioural specifications of imperative languages, postconditions may refer to the prestate of the function, usually with an old operator. Therefore, code performing runtime verification has to record prestate values required to evaluate the postconditions, typically by copying part of the memory state, which causes severe verification overhead, both in memory and CPU time. In this paper, we consider the problem of efficiently capturing prestates in the context of Ortac, a runtime assertion checking tool for OCaml. Our contribution is a postcondition transformation that reduces the subset of the prestate to copy. We formalize this transformation, and we provide proof that it is sound and improves the performance of the instrumented programs. We illustrate the benefits of this approach with a maze generator. Our benchmarks show that unoptimized instrumentation is not practicable, while our transformation restores performances similar to the program without any runtime check.