In this paper, we propose a novel half duplex relaying protocol which belongs to the class of hybrid decode and forward schemes, and we study its performance in the context of communications over slow fading channels. Our protocol is based on a Decode or Quantize and Forward (DoQF) approach. In slow fading contexts, the outage probability Po is of central importance. As the exact evaluation of the outage probability for all possible values of the signal-to-noise ratio (SNR) is a difficult problem for most relaying protocols, we analyze the behaviour of Po as the SNR rho tends to infinity. In that case, rho2Po converges to a constant xi, which we will refer to as the outage gain. The proposed DoQF protocol is shown to outperform the classical DF protocol in terms of outage gain. Moreover, at high SNR, the proposed scheme is shown to be optimal in the wide class of hybrid DF protocols.