Convolutional codes have been widely studied and used in many systems. As the number of memory elements increases, frame error rate (FER) improves but computational complexity increases exponentially. Recently, decoders that achieve reduced average complexity through list decoding have been demonstrated when the convolutional encoder polynomials share a common factor that can be understood as a CRC or more generally an expurgating linear function (ELF). However, classical convolutional codes avoid such common factors because they result in a catastrophic code. This paper provides a way to access the complexity reduction possible with list decoding even when the convolutional encoder polynomials do not share a common factor. Decomposing the original code into component codes that fully exclude some polynomials can allow an ELF to be factored from each component. Parallel list decoding of the component codes can often find the ML codeword. Including a fallback to regular Viterbi decoding yields excellent FER performance while requiring less average complexity than always performing Viterbi on the original trellis. Component codes that have a shared polynomial allow even greater complexity reduction.