  We present the first solvable non-conservative sandpile-like critical model
of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by
Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345
(1998)] that a lack of conservation in the microscopic dynamics of an SOC-model
can be compensated by introducing an external drive and thereby re-establishing
criticality. The model shown is critical for all values of the conservation
parameter. The analytical derivation follows the lines of Broeker and
Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)]
and is supported by numerical simulation. In the limit of vanishing
conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.
