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Some parallel algorithms have the property that, as they are allowed to take more time, the total work that they do is reduced. This paper describes several algorithms with this property. These algorithms solve important problems on directed graphs, including breadth-first search, topological sort, strong connectivity, and and the single source shorest path problem. All of the algorithms run on the EREW PRAM model of parallel computer, except the algorithm for strong connectivity, which runs on the probabilistic EREW PRAM.