We study the following problem: given a strongly connected digraph, find a minimal strongly connected spanning subgraph of it. Our main result is a parallel algorithm for this problem, which runs in polylog parallel time and uses O(n3) processors on a PRAM. Our algorithm is simple and the major tool it uses is computing a minimum-weigh branching with zero-one weights. We also present sequential algorithms for the problem that run in time (m+ n * log n).