A new concept of asymmetric modulation indices has recently been proposed and applied to full response multi-H phase-coded modulations (MHPM) with linear phase pulse function, and improved error probability performance has been found. In the paper, the above concept is extended in two directions. The partial response performance is analysed and compared with full response systems, and the effect of different phase pulse functions on bandwidthlpower efficiency is discussed in detail. It is shown that not only is improved performance possible, but also a full range of design trade-offs, among bandwidth and power efficiencies and complexity, are available for system optimisation.