In this work, efficient protocols are studied for full-duplex relaying (FDR) with loopback interference over Nakagami-m block fading channels. Recently, a selective decodeand- forward (DF) protocol was proposed for FDR, and was shown to outperform existing protocols in terms of outage over Rayleigh-fading channels. In this work, we propose an incremental selective DF protocol that offers additional power savings, yet yields the same outage performance. We evaluate their outage performance over independent non-identically distributed Nakagami-m fading links, and study their relative performance in terms of the signal-to-noise ratio cumulative distribution function via closed-form expressions. The offered diversity gain is also derived. In addition, we study their performance relative to their half-duplex counterparts, as well as known non-selective FDR protocols. We corroborate our theoretical results with simulation, and confirm that selective cooperation protocols outperform the known non-selective protocols in terms of outage. Finally, we show that depending on the loopback interference level, the proposed protocols can outperform their half-duplex counterparts when high spectral efficiencies are targeted.