It was formerly demonstrated that virtually all reasonable exhaustive serial, and a more constrained set of parallel, models cannot predict critical effects associated with self-terminating models. The present investigation greatly generalizes the parallel class of models covered by similar "impossibility" theorems. Specifically, we prove that if an exhaustive parallel model is not super capacity, and if targets are processed at least as fast as non-targets, then it cannot predict such (self-terminating) effects. Such effects are ubiquitous in the experimental literature, offering strong confirmation for self-terminating processing.