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A class of smoothed phase modulation codes is analyzed in terms of power spectral density and error probability for large signal-to-noise ratios. The signals have constant envelope and the information-carrying phase function is of multi-h partial response continuous phase type. A cyclic variation of modulation index from symbol time interval to symbol time interval is introduced. Coherent transmission and an additive white Gaussian channel are assumed. Both power- and bandwidth-efficient signals are to be found in the above class. Comparisons are made between fixed-h and multi-h systems both for the binary and multilevel cases. Tradeoff is performed between bandwidth and error probability performance for large signal-to-noise ratios. It is concluded that quaternary and octal systems always seem preferable. Increasing the number of modulation indexes from one in the fixed-h case to two in the simplest multi-h case gives performance advantages at the expense of increased system complexity.