Two decoding algorithms are introduced for the decoding of multi-level coded modulation and other types of coded modulation involving component codes and interleaving operations. An improved hard iterative decoding (IHID) algorithm is presented that improves upon a hard iteration decoding technique by adding a stopping criterion. Also, a list Viterbi hard iteration decoding (LV-IHID) algorithm is presented that employs list decoding in conjunction with the IHID algorithm. Both of these decoding algorithms improve upon conventional multi-stage decoding by reducing the effective error multiplicity that is observed at the lowest coding level. It is demonstrated that the LV-IHID algorithm performs close to soft iterative decoding. The computational and delay complexity of the proposed decoding algorithms compare favorably with soft iterative decoding strategies. Also, a novel labeling strategy for MLC design is presented.