Results of optimum modulation and coding for MPSK and MDPSK signals transmitted over fading channels and subject to high level interference are presented. The author uses the exact expressions of the probability of error for the uncoded M-ary modulations. However, the analysis of optimum diversity (repetition code) is carried out by a Chernoff bound approximation. Simple expressions are derived to determine the optimum modulation and diversity in terms of the channel parameters. To examine the validity of approximations used throughout, exact analysis of the coded bit-error rate is found numerically, and the results are compared. It is concluded that the exact and the Chernoff bound analysis yield the same results for the optimum modulation and coding and there exist an optimum modulation and coding for each value of signal-to-noise ratio. The results are particularly useful for power and bandwidth limited channels.