We suggest a simple deterministic approximation for the growth of the favored-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitchhiking. Only when Ns<10 (N is the population size and s denotes the selection coefficient) are discrepancies between our approximation and direct numerical simulations of a Moran model notable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.