Satisficing planning aims at generating plans that are not necessarily optimal. Often, minimising plan generation time negatively affects quality of generated plans. Acquiring plans quickly might be of critical importance in decision-making systems that operate nearly in realtime. However, (very) suboptimal plans might be expensive to execute and more prone to failures. Optimising plans after they are generated, in a spare time, can improve their quality. This paper focuses on speeding up the (Greedy) Action Elimination methods, which are used for identifying and removing redundant actions from plans in polynomial time. We present two enhancements of these methods: Plan Action Landmarks, actions that are not redundant in a given plan, and Action Cycles which are subsequences of actions which if removed do not affect the state trajectory after the last action of the cycle. We evaluate the introduced methods on benchmark problems from the Agile tracks of the International Planning Competition and on plans generated by several state-of-the-art planners, successful in the recent editions of the competition.