Distributed priority-based mutual exclusion algorithms may present starvation for low priority requests if the shared resource is continuously asked by high priority requests. To address this problem, several existing algorithms dynamically increment the priority of pending low-priority requests. The drawback of this approach is that it may lead to a great number of priority inversions, i.e., a pending request p is satisfied before another one whose priority is higher than p's. One solution to reduce this number, as we have proposed in [7], is to both postpone priority increments and prevent low priorities from increasing too fast. However, in this case, the response time of low priorities may considerably increase. Therefore, in this article, we propose a new algorithm, denoted "Awareness", which aims at reducing the maximum response time whereas the number of priority violations remains low. To this end, a global view of pending requests of the system is necessary. Performance evaluation results confirm that our new algorithm provides a good tradeoff between response time and number of priority inversions.