Recent advances in the application of the polymerase chain reaction make it possible to score individuals at a large number of loci. The RAPD (random amplified polymorphic DNA) method is one such technique that has attracted widespread interest. The analysis of population structure with RAPD data is hampered by the lack of complete genotypic information resulting from dominance, since this enhances the sampling variance associated with single loci as well as induces bias in parameter estimation. We present estimators for several population-genetic parameters (gene and genotype frequencies, within- and between-population heterozygosities, degree of inbreeding and population subdivision, and degree of individual relatedness) along with expressions for their sampling variances. Although completely unbiased estimators do not appear to be possible with RAPDs, several steps are suggested that will insure that the bias in parameter estimates is negligible. To achieve the same degree of statistical power, on the order of 2 to 10 times more individuals need to be sampled per locus when dominant markers are relied upon, as compared to codominant (RFLP, isozyme) markers. Moreover, to avoid bias in parameter estimation, the marker alleles for most of these loci should be in relatively low frequency. Due to the need for pruning loci with low-frequency null alleles, more loci also need to be sampled with RAPDs than with more conventional markers, and some problems of bias cannot be completely eliminated.