This work investigates the optimization of power allocation for hybrid-ARQ (H-ARQ) retransmissions of non-Gaussian inputs over a bank of independent parallel Gaussian channels. We establish a general solution for maximizing generic transceiver objective utility functions that are monotonically non-decreasing and concave function with respect to the accumulated signal to noise ratio (SNR). Specifically, we investigate optimized solutions under two performance metrics, namely, the mutual information (MI) and the union bound of symbol error rate (UBSER) under maximal ratio combining (MRC) reception. We establish that efficient utilization of parallel channels in H-ARQ retransmissions requires sequential updating of signal-channel pairing as well as optimizing power allocation. Applying geometric analysis of power loading for H-ARQ retransmission, we show that for i.i.d. inputs that are not necessarily Gaussian, the optimum pairing policy should match signals of the lowest cumulative signal-to-noise ratio with channels of the best quality in each transmission, which is consistent with a similar result of , for Gaussian input signals. We further propose a generalized mercury/waterfilling algorithm for the optimal power assignment problem in H-ARQ. Simulation results illustrate substantial improvements over designs based on Gaussian input assumptions.