A new unified family of models for incompressible, steady state magnetic reconnection in a finite region is presented. They are obtained by expanding in powers of the Alfv¿n Mach number and may be used to elucidate some of the puzzling properties of numerical experiments on reconnection which are not present in the classical models. The conditions imposed on the inflow boundary of the finite region determine which member of the family occurs. Petscheklike and Sonneruplike solutions are particular members. The Sonneruplike regime is a special case of a weak slow mode expansion in the inflow region, and it separates two classes of members with reversed currents. These are the hybrid regime with a mixture of strong fast mode and slow mode expansions and the flux pileup regime with a stong slow mode expansion, in which the magnetic field strength increases as it approaches the diffusion region and the flow diverges. The Petscheklike regime is a singular case of a weak fast mode expansion, and it separates the hybrid regime from a regime of slow mode compressions. The hybrid expansions are fast mode in character in the center of the inflow and slow mode near the edges of the region, while the flux pileup expansions possess long thin diffusion regions and no maximum reconnection rate. The maximum rate is calculated for the other solutions as a function of the magnetic Reynolds number and compared with the classical Sweet-Parker and Petschek rates. For the flux pileup and hybrid regimes, reconnection can be ;much faster than the maximum Petschek rate. Care should be taken in deciding which type of reconnection is operating in a numerical experiment. Indeed, no experiment to date has used boundary conditions appropriate for demonstrating steady state Petschek reconnection.