This paper proposes an extension of the discrete Lighthill–Whitham–Richards model of the cell transmission model type to reproduce capacity drop and the propagation of jam waves. Recent studies have tried to incorporate the capacity drop into discrete first-order traffic flow models for traffic optimization purposes. It was found that the inflow to a discharging cell predicted by these models might have been overestimated, and this overestimation influenced the propagation of a jam wave. An empirical analysis was carried out to confirm this assumption. It was found that the extent of the flow reduction depended on the state difference between the targeting cell and its upstream cell. On the basis of these findings, a new mathematical model formulation is given. Simulations with both a hypothetical freeway stretch and a real-life freeway stretch are performed to test the behavior of the proposed model. The previously mentioned models are also simulated for comparison. The simulation results indicate that the proposed model is better able to reproduce jam waves. In addition, the proposed model can be used in a linear model predictive control framework and formulated as a linear optimization problem, which may be beneficial for a real-life, real-time application.