Abstract The performance of an underlay cognitive radio network that coexists with a primary destination is studied in terms of the outage probability. The investigated secondary network comprises a source-destination pair communicating under the assistance of a full-duplex decode-and-forward relay. We consider the following key aspects pertinent to the underlay cognitive-radio approach and to the fullduplex operation at the relay: the transmit power constraint of the cognitive network by the maximum interference tolerated at the primary destination, as well as by the maximum-available transmit power at the cognitive terminals; the impact of the residual self-interference inherent to the relay; and the use of a joint-decoding technique at the destination in order to combine the concurrent signals coming from the source and relay, which enables the treatment of the direct-link transmission as information signal, rather than as interference. Herein, the joint effect of the maximum interference power constraint and the residual self-interference are both examined. To this end, an arbitrary power allocation between source and relay is allowed. Then, an accurate closed-form approximation to the outage probability is proposed, from which an asymptotic expression is derived for the high SNR ratio regime. Our analytical results are validated via Monte Carlo simulations. Importantly, we show that a maximum-available transmit power not only saves energy but also reduces the outage probability at medium to high SNR ratio.