A non-regenerative dual-hop wireless system based on a distributed space-time-coding strategy is considered. It is assumed that each relay retransmits an appropriately scaled space-time coded version of received signals. The main goal of this paper is to investigate a power allocation strategy in relay stations using analytical and simulation arguments to satisfy the quality of service requirements. In the high signal-to-noise ratio regime for the relay-destination link, it is shown that the optimum power allocation strategy in each relay which minimizes the outage probability is to remain silent, if its channel gain with the source is less than a prespecified threshold level. The Monte-Carlo simulations show that the near-optimal power allocation scheme in each relay in order to minimize the outage probability or the frame-error rate is the threshold-based on-off power scheme. Also, the numerical results demonstrate a dramatic improvement in the system performance by using this scheme compared to the case that the relay stations forward their received signals with full power. Finally, a hybrid amplify-and-forward/detect-and-forward scheme is numerically evaluated.