There is considerable interest in computational methods to assist in the use of genetic polymorphism data for locating disease-related genes. Haplotypes, contiguous sets of correlated variants, may provide a means of reducing the difficulty of the data analysis problems involved. The field to date has been dominated by methods based on the "haplotype block" hypothesis, which assumes discrete population-wide boundaries between conserved genetic segments, but there is strong reason to believe that haplotype blocks do not fully capture true haplotype conservation patterns. In this paper, we address the computational challenges of using a more flexible, block-free representation of haplotype structure called the "haplotype motif" model for downstream analysis problems. We develope algorithms for htSNP selection and missing data inference using this more generalized model of sequence conservation. Application to a dataset from the literature demonstrates the practical value of these block-free methods.