Our aim is to formalize models for high-resolution haplotype structure in such a way that they can be useful in statistical methods for LD mapping. Some steps in that direction have been taken by Daley et al. ‘01, who outline a hidden Markov model (HMM) that allows for common haplotypes in each block. We propose somewhat different models that also use HMM. In this talk, we address the problem of assessing goodness of fit of particular models, where each model involves choices such as number and positions of blocks and common haplotypes in each block. Our models also allow for haplotypes in a block that are not one of the common types. We discuss choice of goodness-of-fit statistic, parametrization, and computational issues involved in assessing the fit of background LD models to data.