We introduce a family of lattice-gas models of flocking. whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C. https://www.roneverhart.com/MagnaFlow-2003-2006-Toyota-Corolla-Street-Series-Cat-Back-Performance-Exhaust-System/