We propose that an appropriate prototype for modeling self-organized criticality in dissipative systems is a generalized version of the two-variable cellular automata model introduced by Hergarten and Neugebauer [Phys. Rev. E 61, 2382 (2000)]. We show that the model predicts exponents for the event size distribution which are consistent with physically observed results for dissipative phenomena such as earthquakes. In addition we provide evidence that the model is critical based on both scaling analyses and direct observation of the distribution and behavior of the two variables in the interior of the lattice. We further argue that for reasonably large lattices the results are universal for all dissipative choices of the model parameters. © 2005 The American Physical Society.