We presents a self-stabilizing algorithm for the unison problem which achieves an efficient trade-off between time, workload and space in a weak model. Our algorithm is defined in the atomic-state model and works in a simplified version of the stone age model in which networks are anonymous and local ports are unlabelled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon. Assuming a period B ≥ 2D + 2, our algorithm stabilizes in at most 2D − 2 rounds and O(min(n 2 B, n 3)) moves, while using ⌈log B⌉ + 2 bits per node where D is the network diameter and n the number of nodes. In particular and to the best of our knowledge, it is the first self-stabilizing unison for arbitrary anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node. Finally, we show that our solution allows to efficiently simulate synchronous self-stabilizing algorithms in an asynchronous environment. This provides new state-of-the-art algorithm solving both the leader election and the spanning tree construction problem in any identified connected network which, to the best of our knowledge, beat all known solutions in the literature.