A coded (1-D) system containing a punctured convolutional encoder is analyzed. In general, a punctured encoder with 2v states results in a decoder trellis with 2v+1 states and a periodically time-varying branch structure. A class C of punctured convolutional encoders for which the decoder trellis has a fixed branch structure with 2v states is described. An encoder in this class can be combined with a precoder to form a new punctured convolutional encoder that generates the output from the precoder. The author determines the set of good variable-rate trellis codes for selectable rate encoding and Viterbi decoding. A set of variable-rate trellis codes is generated by a variable-rate punctured convolutional encoder in C. The author also determines punctured convolutional encoders in C that generate a single good high-rate trellis code.