We evaluate the outage performance in a three-terminal full-duplex relay channel that adopts a selective decode-and-forward protocol, taking relay self-interference into account. Previous work focused on coverage extension scenarios where direct source-destination transmissions are neglected or considered as interference. In this work, we account for the relay self-interference, and exploit the cooperative diversity offered by the independently fading source/relay message replicas that arrive at the destination. We present an approximate, yet accurate, closed-form expression for the end-to-end outage probability that captures their joint effect. With the derived expression in hand, we propose a relay transmit power optimization scheme that only requires the relay knowledge of channel statistics. Finally, we corroborate our analysis with simulations.