It is known that convolutional coding and Viterbi decoding together with high-level modulation can provide error-control protection without sacrificing bandwidth efficiency on additive white Gaussian noise (AWGN) channels. Bearing this in mind, the paper is concerned with the performance of short constraint length convolutional codes in conjunction withM-ary phase-shift-keyed modulation and maximum-likelihood Viterbi decoding on the fully interleaved Rician fading channels. The primary interest is in the bit error probability performance as a function of system parameters and channel parameters. The generating function union bounding approach is applied, and fairly general analytic upper bounds on the event and bit error probability performance are developed. The bit error probability performance of selected rate-1/2 optimum codes with QPSK and of selected rate-2/3 Ungerbock codes and the Hui code with 8PSK are evaluated using the developed bound. The tightness of the analytic upper bound on bit error probability is also checked by means of computer simulation.