Short-period comets with P ≤ 15 yr represent one of the most complete comet samples. The magnitude distribution of these comets was analysed using a maximum likelihood method. The brightness (magnitude) index for the comets with H 10 ≤ 11 mag was estimated together with the large sample errors and found to be 0.62 ± 0.09. It was clear that many faint comets with H 10 > 11 mag remain to be discovered. Some of the faint, smaller comets have probably been removed from the distribution altogether. Observational selection was also apparent for the sample of comets with perihelia q < 1.5 AU. It was found that comets satisfying the combined criteria P ≤ 15 yr, H 10 ≤ 11 mag, q < 1.5 AU probably represent the most complete set of comets available. The brightness index of this sample estimated by maximum likelihood was 0.69 ± 0.14. This translates into a mass distribution index s of 1.69 ± 0.14 indicating that most of the mass is contained in a few of the larger comets rather than spread throughout the smaller ones. This distribution, although modified by mass loss, is most likely to have been produced by a process of particle accretion.