In this study, schemes for optimisation of power allocation (OPA) for asymmetric relay placement are presented for multi-hop communication in a Rayleigh-fading environment. For a decode-and-forward (DF) multi-hop communication system, expressions are derived for optimised power allocation based on symbol error probability (SEP) and global channel state information (GCSI). The analysis for OPA based on GCSI is extended to a hybrid combination of amplify-and-forward (AF) and DF relays. Analysis is done for two kinds of modulation schemes: M-ary phase-shift keying with coherent detection and orthogonal M-ary frequency-shift keying with non-coherent detection. Simulation results show that for a multi-hop system with asymmetric relay placement, power optimisation schemes perform better than the conventional equal power allocation scheme. In addition, power optimisation based on GCSI shows substantially improved performance compared with power allocation based on end-to-end SEP. Further, performance comparison is shown for increase in number of relay nodes in an AF and DF multi-hop system with and without power allocation. The performance of a DF system improves with increase in number of relay nodes whereas performance of an AF system degrades. Hybrid relaying provides an option to exercise switching between DF and AF so as to extract the maximum advantage of the two relaying schemes.