Chandra and Toueg have proposed a new approach to overcome the impossibility of reaching deterministically Consensus in asynchronous systems subject to crash failures. They augment the asynchronous model with unreliable failure detectors. In this paper, we present an extension of an algorithm that they proposed to solve consensus using \Diamond \cal S failure detectors. We argue that this extension is a simple and efficient building block which can be used to solve various agreement problems. We consider a particular agreement problem, namely the Non-Blocking Atomic Commitment problem and we show the advantages of our solution by comparing it to other classical approaches.