This paper studies the impact of the energy efficiency design index (EEDI) on very large crude carriers’ (VLCCs) CO2 emissions. In competitive sectors such as the VLCC market, this analysis must be performed over a market cycle adjusting a ship's steaming speed to the market rate and bunker cost. Our numbers indicated that, over a market cycle, imposition of EEDI will result in a slight increase in VLCC CO2 emissions, relative to no regulation at all. The problem is two-fold: (1) For VLCCs, EEDI effectively limits installed power. But at current and expected Bunker Fuel Oil prices, a non-EEDI VLCC owner uses all his installed power only in a full boom. For the great bulk of her life, a non-EEDI VLCC uses little or no more power than an EEDI-compliant ship. (2) In limiting installed power, EEDI induces owners to use smaller bore, higher revolutions-per-minute engines. These engines have a higher specific fuel consumption and, more importantly, require a smaller and less efficient propeller. This means the EEDI-compliant VLCC consumes more fuel when the market is not in boom, which is 90% of the time. In contrast, we find that a $50 per ton CO2 bunker tax will reduce VLCC CO2 emissions by more than 6% over a market cycle. Moreover, it will do so without forcing the world to devote 30% more resources to a greatly expanded, under-powered, overdriven VLCC fleet.