In this paper, a rate k/n punctured convolutional code is considered as a time-varying code with period k. The punctured convolutional codes with time-varying constraint length are studied. For these codes, new maximum likelihood decoding techniques are proposed. Not only for the binary symmetric channel but also for any discrete memoryless channel, these decoding techniques can periodically reduce the number of survivors and comparisons in the decoding process. On the basis of the proposed decoding techniques, new classes of punctured convolutional codes are introduced. Computer searches are perfermed to construct good codes from these classes.