In asynchronous distributed systems it is very hard to assess if one of the processes taking part in a computation is operating correctly or has failed. To overcome this problem, distributed algorithms are created using unreliable failure detectors that capture in an abstract way timing assumptions necessary to assess the operating status of a process. One particular type of failure detector is a leader election, that indicates a single process that has not failed. The unreliability of these failure detectors means that they can make mistakes, however if they are to be used in practice there must be limits to the eventual behavior of these detectors. These limits are defined as the quality of service (QoS) provided by the detector. Many works have tackled the problem of creating failure detectors with predictable QoS, but only for crash-stop processes and synchronous systems. This paper presents and analyzes the behavior of a new leader election algorithm named NFD-L for the asynchronous crash-recovery failure model that is efficient in terms of its use of stable memory and message exchanges.