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The delay till success (DTS) is the mean number of transmissions needed, averaged over the fading, until a single packet is successfully received (decoded) over a wireless link. This paper shows that under a mean and a peak power constraint, random power control can significantly reduce the DTS. We derive the optimal power control policies that minimize the DTS at one link of given length. For most commonly used fading distributions, these optimal power control policies are random on-off policies, whose parameters depend on the fading statistics and the link distance. We present two applications of this result in the context of noise-limited wireless networks: minimizing the local delay (mean delay for successful nearest-neighbor communication) and minimizing the local anycast delay (mean delay for a transmission to any node).