This paper deals with the trade-off between time, workload, and versatility in self-stabilization, a general and lightweight fault-tolerant concept in distributed computing. In this context, we propose a transformer that provides an asynchronous silent self-stabilizing version Trans(AlgI) of any terminating synchronous algorithm AlgI. The transformed algorithm Trans(AlgI) works under the distributed unfair daemon and is efficient both in moves and rounds. Our transformer allows to easily obtain fully-polynomial silent self-stabilizing solutions that are also asymptotically optimal in rounds. We illustrate the efficiency and versatility of our transformer with several efficient (i.e., fully-polynomial) silent self-stabilizing instances solving major distributed computing problems, namely vertex coloring, Breadth-First Search (BFS) spanning tree construction, k-clustering, and leader election.