Confusion network decoding has proven to be one of the most successful approaches to machine translation system combination. The hypothesis alignment algorithm is a crucial part of building the confusion networks and many alternatives have been proposed in the literature. This paper describes a systematic comparison of five well known hypothesis alignment algorithms for MT system combination via confusion network decoding. Controlled experiments using identical pre-processing, decoding, and weight tuning methods on standard system combination evaluation sets are presented. Translation quality is assessed using case insensitive BLEU scores and bootstrapping is used to establish statistical significance of the score differences. All aligners yield significant BLEU score gains over the best individual system included in the combination. Incremental indirect hidden Markov model and a novel incremental inversion transduction grammar with flexible matching consistently yield the best translation quality, though keeping all things equal, the differences between aligners are relatively small.