The topic of this paper is the estimation of alignments and mutation rates based on stochastic sequence-evolution models that allow insertions and deletions of subsequences (fragments) and not just single bases. The model we propose is a variant of a model introduced by Thorne et al., (J. Mol. Evol., 34, 3-16, 1992). The computational tractability of the model depends on certain restrictions in the insertion/deletion process, possible effects we discuss.