In this paper we study the computational complexity of postoptimizing partially ordered plans, i.e., we investigate the problem that is concerned with detecting and deleting unnecessary actions. For totally ordered plans it can easily be tested in polynomial time whether a single action can be removed without violating executability. Identifying an executable subplan, i.e., asking whether k plan steps can be removed, is known to be NP-complete. We investigate the same questions for partially ordered input plans, as they are created by many search algorithms or used by real-world applications – in particular time-critical ones that exploit parallelism of non-conflicting actions. More formally, we investigate the computational complexity of removing an action from a partially ordered solution plan in which every linearization is a solution in the classical sense while allowing ordering insertions afterwards to repair arising executability issues. It turns out that this problem is NP-complete – even if just a single action is removed – and thereby show that this reasoning task is harder than for totally ordered plans. Moreover, we identify the structural properties responsible for this hardness by providing a fixed-parameter tractability (FPT) result.