The flux of comets with semimajor axes approximately 20 000 AU in the outer planetary region is estimated on the presumption that the major planets and the galactic tide control the dynamics of comets. The flux is found to be a rapidly increasing function of q, the perihelion distance. The supply rate is given by n(SP) = (0.0015 approximately 0.003) n-LP, where n-LP is the flux of comets which have semimajor axes between 10 000 and 20 000 AU before entering the planetary region. If the lifetime of short-period (SP) comets is typically 2 x 10(4) yr, it would be possible to regard SP comets as originating from the Oort cloud. If, however, it is as short as 2 x 10(3) yr there is a discrepancy of a factor 10 between the observed and predicted supply rates. The effects of factors such as the discovery probability and magnitude difference between long-period (LP) and SP comets are discussed.