This paper studies power allocation for performance constrained dual-hop variable-gain amplify-and-forward (AF) relay networks in Nakagami-Formula Omitted fading. In this context, the performance constraint is formulated as a constraint on the end-to-end signal-to-noise-ratio (SNR) and the overall power consumed is minimized while maintaining this constraint. This problem is considered under two different assumptions of the available channel state information (CSI) at the relays, namely full CSI at the relays and partial CSI at the relays. In addition to the power minimization problem, we also consider the end-to-end SNR maximization problem under a total power constraint for the partial CSI case. We provide closed-form solutions for all the problems which are easy to implement except in two cases, namely selective relaying with partial CSI for power minimization and SNR maximization, where we give the solution in the form of a one-variable equation which can be solved efficiently. Numerical results are then provided to characterize the performance of the proposed power allocation algorithms considering the effects of channel parameters and CSI availability.