As genetic marker maps have improved, multipoint linkage analysis has become a crucial part of all disease mapping studies. Paradoxically, multipoint lod scores become increasingly difficult to compute, particularly as the numbers of markers, marker alleles and untyped people increase. We have solved this problem by using a novel set-recording scheme to recode each person's genotype and 'fuzzy inheritance' to infer transmission probabilities. Our approach is implemented in a memory-efficient computer program, VITESSE, for extremely rapid computation of exact multipoint likelihoods. VITESSE enables fast and precise multipoint mapping of disease loci with highly polymorphic markers.