Congestion pricing is seen as an effective policy to address traffic congestion. In such policies where money, people and authorities are involved, the success generally hinges upon two factors: equity (being fair) and acceptability (to both people and authorities). The primary concern is the equity, for which “tradable credit scheme (TCS)” has been introduced and extensively studied in the literature. Nevertheless, due to the complexity of the trading schemes, the TCS has yet to find any foot in the real world. To this end, a novel idea of rewarding has substituted the trading component to be known as toll-and-subsidy scheme (TSS). The idea is to charge the drivers on some roads (toll) while rewarding them to use other alternative—and perhaps underutilized—roads (subsidy). The research of the TSS is in its infancy stage. The problem to be tackled in this study is as follows: Given a set of roads constituting a cordon line around the central business district (CBD) or across a screen line, how much toll or subsidy should be assigned to each road? The problem is first transformed into a capacitated traffic assignment problem. We employ a solution method based on augmenting the travel time of roads up to the level at which the traffic volumes do not exceed some target rates. A real dataset from the city of Winnipeg, Canada, is used as a pilot study. We then discuss policy-related applications of the TSS. It is proved in the literature that one can obtain optimal TSSs for various objectives and considerations. To this end, the non-negativity of the toll values is relaxed which results in a valid toll set. Nevertheless, the computational time is found to be of highest significance. Our method differs in the fact that the traffic volumes are bounded from the above and it is quite affordable. The main contribution is first to highlight the concept of subsidy along with traditional thought of merely toll. Second is to interpret the Lagrangian values of the capacity constraints as the values of the toll/subsidy.