In this paper, we consider the classical bandwidth efficiency improvement technique which is the partial response signaling (PRS), especially 1 + D duobinary signaling, for M-ary phase shift keying (MPSK) modulation transmitted over fading channels. We only consider the case where interleaving/deinterleaving is employed to further combat the fading and assume that the ideal channel state information is available. Analytical bit error probability upper bounds are derived using the transfer function bounding technique for both the partial response coded and uncoded MPSK cases. One interesting result, obtained from the comparisons, is that the partial response coded MPSK outperforms the uncoded MPSK in the fading environment, for signal-to-noise ratio values greater than a threshold, when the soft decision Viterbi decoder is used, contrasting to the additive white gaussian noise channels. In order to demonstrate the validity of this result, the asymptotic bit error probability expression for trellis codes in the presence of fading, given in , is considered. Computer simulations done for the Rayleigh fading case, also verify this aspect of the partial response signaling.