The classical Petschek model of fast, steady state reconnection has been generalized in two families of reconnection regimes. The first family, which we refer to as ''almost uniform,'' models the reconnection of nearly uniform, antiparallel magnetic fields, and it includes Petschek's model as a special case. The second family, which we refer to as nonuniform, models the reconnection of strongly curved magnetic fields, and it includes separatrix jets and reversed current spikes at the ends of the diffusion region. In general, both families contain regimes having fast reconnection rates, but we show here that these fast reconnection regimes do not occur when the boundary conditions often used in numerical experiments are adopted. In 1986, D. Biskamp carried out a series of numerical experiments to check Petschek's prediction that the maximum reconnection rate should scale with the magnetic Reynolds number, Rme, as [ln(Rme)>-1. Biskamp found that the maximum reconnection rate in his experiments did not scale in this way but instead as Rme-1/2. Because this corresponds to the scaling predicted by the slow reconnection theory of Sweet (1958) and Parker (1957), Biskamp has argued that his numerical experiments show that fast reconnection does not exist at high magnetic Reynolds numbers. However, by applying boundary conditions similar to Biskamp's to the ''nonuniform'' family of reconnection regimes, we are able to explain Biskamp's scaling results and to explain why he did not achieve fast reconnection in his numerical experiments. Therefore, we conclude that numerical experiments with suitably designed boundary conditions are highly likely to exhibit fast reconnection and that such reconnection is a common process in astrophysical and space plasmas. ¿ American Geophysical Union 1992