Desktop Grids have proved to be a suitable platform for the execution of Bag-of-Tasks applications but, being char- acterized by a high resource volatility, require the avail- ability of scheduling techniques able to effectively deal with resource failures and/or unplanned periods of unavailabil- ity. Fault-aware scheduling, proposed in [2], can be consid- ered a promising approach, yielding to both performance improvements for Bag-of-Task-Applications and increased utilization for Desktop Grids. The best fault-aware schedul- ing strategy available at the moment uses on-line schedul- ing, that is it starts a task as soon as a machine becomes available. In this paper we present a machine selection policy based on the idea that sometimes is better to wait for another machine rather than greedily exploit an im- mediately available one. An extensive simulation study, carried on for a variety of realistic Desktop Grid config- urations and Bag-of-Task workloads, has revealed that the new scheduling strategy further improve application perfor- mance and machine utilization with respect to the best fault- aware scheduling strategy among those proposed in [2].