Decision makers facing emission-reduction targets need to decide which abatement measures to implement, and in which order. This paper investigates how marginal abatement cost (MAC) curves can inform such a decision. We re-analyse a MAC curve built for Brazil by 2030, and show that misinterpreting MAC curves as abatement supply curves can lead to suboptimal strategies. It would lead to (i) under-investment in expensive, long-to-implement and large-potential options, such as clean transportation infrastructure, and (ii) over-investment in cheap but limited-potential options such as energy-efficiency improvement in refineries. To mitigate this issue, the paper proposes a new graphical representation of MAC curves that explicitly renders the time required to implement each measure. In addition to the cost and potential of available options, designing optimal short-term policies requires information on long-term targets (e.g., halving emissions by 2050) and on the speed at which measures can deliver emission reductions. Mitigation policies are thus best investigated in a dynamic framework, building on sector-scale pathways to long-term targets. Climate policies should seek both quantity and quality of abatement, by combining two approaches. A "synergy approach" that focuses on the cheapest mitigation options and maximizes co-benefits. And an "urgency approach" that starts from a long-term objective and works backward to identify actions that need to be implemented early. Accordingly, sector-specific policies may be used (i) to remove implementation barriers on negative- and low-cost options and (ii) to ensure short-term targets are met with abatement of sufficient quality, i.e. with sufficient investment in the long-to-implement options required to reach long-term targets.