The TagSNP problem is a specific form of compression problem arising in genetics. Given a very large set of SNP (genomic positions where polymorphism is observed in a given population), the aim is to select a smallest subset of SNPs which represents the complete set of tagSNP reliably. This is possible because strong correlations existing between neighboring SNPs. Typically, besides minimizing the tagSNP set size (mostly for economical reasons), one also seek a maximally informative subset for the given size, generating di erent secondary criteria. This problem, which is also closely related to a set covering problem, can be simply described as a weighted CSP. We report here our experiments with human tag SNP data using a recently designed WCSP algorithm combining the "Russian Doll Search" algorithm with local consistency for cost functions and an active exploitation of the problem structure, through a tree decomposition of the problem.