How should carbon be taxed as a part of fiscal policy? The literature on optimal carbon pricing often abstracts from other taxes. However, when governments raise revenues with distortionary taxes, carbon levies have fiscal impacts. While they raise revenues directly, they may shrink the bases of other taxes (e.g., by decreasing employment). This paper theoretically characterizes and then quantifies optimal carbon taxes in a dynamic general equilibrium climate-economy model with distortionary fiscal policy. First, this paper establishes a novel theoretical relationship between the optimal taxation of carbon and of capital income. This link arises because carbon emissions destroy natural capital: They accumulate in the atmosphere and decrease future output. Consequently, this paper shows how the standard logic against capital income taxes extends to distortions on environmental capital investments. Second, this paper characterizes optimal climate policy in sub-optimal fiscal settings where income taxes are constrained to remain at their observed levels. Third, this paper presents a detailed calibration that builds on the seminal DICE approach (Nordhaus, 2008) but adds features essential for a setting with distortionary taxes, such as a differentiation between climate change production impacts (e.g., on agriculture) and direct utility impacts (e.g., on biodiversity existence value). The central quantitative finding is that optimal carbon tax schedules are 8% – 24% lower when there are distortionary taxes, compared to the setting with lump-sum taxes considered in the literature.