Cooperative schemes are promising solutions for cellular wireless systems to improve system fairness, extend coverage and increase capacity. The use of relays is of significant interest to allow radio access in situations where a direct path is not available or has poor quality. A data precoded relay-assisted scheme is proposed for a system cooperating with 2 relays, each equipped with either a single antenna or 2-antenna array. However, because of the half-duplex constraint at the relays, relaying assisted transmission would require the use of a higher order constellation than in the case of a continuous link is available from the BS to the UT. This would imply a penalty in the power efficiency. The simple precoding scheme proposed exploits the relation between QPSK and 16-QAM, by alternately transmitting through the 2 relays, achieving full diversity, while significantly reducing power penalty. Analysis of the pairwise error probability of the proposed algorithm with a single antenna in each relay is derived and confirmed with numerical results. We show the performance improvements of the precoded scheme, relatively to equivalent distributed SFBC scheme employing 16-QAM, for several channel quality scenarios. Numerical results also confirm that the precoded scheme performance is very close to the equivalent non-cooperative SFBC QPSK one, with the direct link available, when all the links have the same quality, even outperforming the latter for the 2 antennas case.