In a recent work, we proposed a simple and efficient power allocation scheme for a dual-hop communication system with multiple lossy-forward relays. In this letter, we propose a less simple, yet more efficient and comprehensive power allocation scheme for the referred system. Unlike our previous approach, which was based on an asymptotic reasoning at high signal-to-noise ratio, the new one optimizes the allocation policy according to any particular amount of total transmit power. The more constrained that amount of power, the more advantageous the new scheme.