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In this study, the authors optimise the outage probability of amplify and forward incremental relaying (IR) scheme using two different power allocation methods in the presence of channel estimation errors. The authors find the outage probability of IR scheme and minimise it subject to traditional power (TP) constraint in which the sum of nodes' powers is fixed and outage-dependent power (ODP) constraint which is compatible with the physical concept of IR and takes into account the quality of the direct path in the optimisation problem. The authors provide closed-form expressions to allocate power to pilot and data symbols of both the source and the relay. Although, their analysis uses high signal-to-noise-ratio (SNR) approximation, the analytical solutions perform very close to optimal ones obtained through global numerical search. The authors show that ODP constraint has substantial superiority over TP constraint, especially when the relay is placed close to the source. Moreover, the authors compare power-optimised IR subject to the mentioned power constraints with equal power allocation scheme and show the impact of power optimisation on the outage performance of IR system.