The stochastic lattice gas introduced in [1] was shown to simulate the one-dimensional Burgers' equation and the phenomena it embodies: travelling shocks and rarefaction waves. However, shock widening not characteristic of the actual solution is intrinsic to the model. In the present contribution, we consider a variant of this lattice model in which shock widening is inhibited. In addition, in [1] we supposed decorrelated occupation probabilities in the lattice system in order to derive the approximate master equation, a finite difference version of Burgers equation. Here we reconsider the master equation, incorporating the effect of the correlation into the derivation. We see that the master equation is in fact a finite difference discretization of the one-dimensional Navier-Stokes equation for incompressible parallel flow. 11.5