This paper presents a new upperbound on the pair-wise error probability of MPSK sequences for the Rayleigh fading channel when channel state information (CSI) is unavailable. This bound is derived by adding weight factors in computing symbol metrics. Simulation results show that the weight factors which optimize the upperbound likely optimize the error rate as well. Multilevel coded MPSK schemes for the Rayleigh fading channel are also devised. Results show that the added weight factors improve the error performances of these schemes in the case that CSI is unavailable.