In their influential Psychological Review article, Bogacz, Brown, Moehlis, Holmes, and Cohen (2006) discussed optimal decision making as accomplished by the drift diffusion model (DDM). The authors showed that neural inhibition models, such as the leaky competing accumulator model (LCA) and the feedforward inhibition model (FFI), can mimic the DDM and accomplish optimal decision making. Here we show that these conclusions depend on how the models handle negative activation values and (for the LCA) across-trial variability in response conservativeness. Negative neural activations are undesirable for both neurophysiological and mathematical reasons. However, when negative activations are truncated to 0, the equivalence to the DDM is lost. Simulations show that this concern has practical ramifications: the DDM generally outperforms truncated versions of the LCA and the FFI, and the parameter estimates from the neural models can no longer be mapped onto those of the DDM in a simple fashion. We show that for both models, truncation may be avoided by assuming a baseline activity for each accumulator. This solution allows the LCA to approximate the DDM and the FFI to be identical to the DDM.