Abstract: The adequate system performance is usually a critical requirement to be checked during the verification phase of a system. Thus, accurately measuring the performance of current industrial systems, which are often modelled as a Discrete Event Systems (DES), is a need. Due to the state explosion problem, the performance evaluation of DES becomes increasingly difficult as the size of the systems increases. Some approaches, such as the computation of performance bounds, have been developed to overcome this problem. In this paper we propose a new method to produce performance bounds that are sharper than the ones that can be achieved with current methods. The core of our method is an iterative algorithm that initially considers the most constraining bottleneck cycle of the system and adds other cycles to it in each iteration. The proposed method is deeply explained and then applied to a broad set of Marked Graphs.