In continuation of our recent combinatorial work on 810 X(2)YZ full Heusler alloys, a computational study of the same class of materials but with the inverse (XY)XZ crystal structure has been performed on the basis of first-principles (GGA) total-energy calculations using pseudopotentials and plane waves. The predicted enthalpies of formation evidence 27 phases to be thermochemically stable against the elements and the regular X(2)YZ type. A chemical-bonding study yields an inherent tendency for structural distortion in a majority of these alloys, and we predict the existence of the new tetragonal phase Fe(2)CuGa (P4(2)/ncm; a = 5.072 A, c = 7.634 A; c/a approximately 1.51) with a saturation moment of mu = 4.69 micro(B) per formula unit. Thirteen more likewise new, isotypical phases are predicted to show essentially the same behavior. Six phases turn out to be the most stable in the inverse tetragonal arrangement. The course of the magnetic properties as a function of the valence-electron concentration is analyzed using a Slater-Pauling approach.