Mobile users with single antennas can still take advantage of spatial diversity through cooperative space-time encoded transmission. In this paper, we consider a scheme in which the relay chooses to cooperate only if the source-relay channel is of an acceptable quality and we evaluate the usefulness of relaying when the source acts blindly and ignores the decision of the relay if it may cooperate or not. In our study, we consider a regenerative relay in which the decision to cooperate is based on a signal-to-noise ratio (SNR) threshold and consider the effect of the possible erroneously detected and transmitted data at the relay. We derive the end-to-end bit-error rate (BER) for binary phase-shift keying modulation and look at two power allocation strategies between the source and the relay in order to minimize the end-to-end BER at the destination for a high SNR. Some selected performance results show that computer simulations based results coincide with our analytical results.