We propose a novel approximate-likelihood method to fit demographic models to human genomewide single-nucleotide polymorphism (SNP) data. We divide the genome into windows of constant genetic map width and then tabulate the number of distinct haplotypes and the frequency of the most common haplotype for each window. We summarize the data by the genomewide joint distribution of these two statistics-termed the HCN statistic. Coalescent simulations are used to generate the expected HCN statistic for different demographic parameters. The HCN statistic provides additional information for disentangling complex demography beyond statistics based on single-SNP frequencies. Application of our method to simulated data shows it can reliably infer parameters from growth and bottleneck models, even in the presence of recombination hotspots when properly modeled. We also examined how practical problems with genomewide data sets, such as errors in the genetic map, haplotype phase uncertainty, and SNP ascertainment bias, affect our method. Several modifications of our method served to make it robust to these problems. We have applied our method to data collected by Perlegen Sciences and find evidence for a severe population size reduction in northwestern Europe starting 32,500-47,500 years ago.