The linear theory of magnetic reconnection demonstrates that the rate of energy release at an X-type neutral point is "fast" - only logarithmically dependent on the plasma resistivity - if the field is strictly two-dimensional, gas pressure is absent, and perturbations are small. The present paper explores the response of the X-point to finite amplitude disturbances under the more realistic conditions of limited compressibility and a finite nonplanar magnetic field component. We show that fast reconnection is not inhibited by large amplitudes of the perturbation - in fact, both the reconnection rate and the ohmic dissipation rate increase with decreasing plasma resistivity. This "super fast" scaling can be understood by a simple, one-dimensional dynamic collapse model. However, the presence of finite gas pressure or an axial magnetic field component stalls the collapse by providing backpressure which retards the imploding magnetic wave: the current sheet is prevented from thinning and reconnection drops toward the static diffusion rate. Thus we overrule the initial implosion as a means of rapidly liberating magnetic energy when gas pressure or an axial magnetic field are present, as they are in the solar corona. But in this case the initial collapse does not provide the complete picture. Gas is subsequently squeezed out of the current sheet, allowing a higher current density to be attained. Thus the possibility of fast reconnection remains open. The dynamics of the evolution are complicated; it is not yet clear under exactly what conditions fast reconnection may be attainable. © 1996. The American Astronomical Society. All rights reserved.