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Relayed transmission is a way to attain broader coverage by splitting the communication link from the source to the destination into several shorter links/hops. One of the main advantages of this communication technique is that it distributes the use of power throughout the hops. This implies longer battery life and lower interference introduced to the rest of the network. In this context, this paper investigates the optimal allocation of power over these links/hops for a given power budget. All hops are assumed to be subject to independent Rayleigh fading. Outage probability which is the probability that the link quality from source to destination falls below a certain threshold is used as the optimization criterion. Numerical results show that optimizing the allocation of power enhances the system performance, especially if the links are highly unbalanced in terms of their average fading power or if the number of hops is large. Interestingly, they also show that nonregenerative systems with optimum power allocation can outperform regenerative systems with no power optimization.