The problem of pressure limitations on the rate of flux pile-up magnetic re
connection is studied. We first examine the recent suggestion of Jardine an
d Allen (1998) for moderating the build-up of magnetic pressure in the curr
ent sheet by considering inflows with nonzero vorticity. An analytic argume
nt shows, however, that unbounded magnetic pressures in the limit of small
resistivities can be avoided only at the cost of unphysical dynamic pressur
es in the plasma. Hence, the pressure limitation on the reconnection rate i
n a low-beta plasma cannot be avoided completely. Nevertheless, we demonstr
ate that reconnection can be more rapid in a new solution that balances the
build-up in dynamic pressure against both the plasma and magnetic pressure
s. This exact MHD solution has the characteristics of merging driven by the
coalescence instability. The maximum energy release rate of the model is c
apable of explaining a modest solar flare.