Fossil fuels can be used with minimal atmospheric emissions of carbon dioxide by capturing and storing the CO2 away in geologic structures. However, stored CO2 can leak back to the atmosphere reducing the utility of this technology. To explore the trade-offs between discounting, leakage, the cost of sequestration and the energy penalty (the energy necessary to capture, transport and inject carbon underground), we derive analytic expressions for the value of leaky CO2 storage compared to perfect storage when storage is a marginal component of the energy system. If the annual leak rate is 1% and the discount rate is 4%, for example, then CO2 mitigation using leaky storage is worth 80% of mitigation with perfect storage. Using an integrated assessment numerical model (DIAM) to explore the role of leakage when CO2 storage is non-marginal, we find that a leakage rate of 0.1% is nearly the same as perfect storage while a leakage rate of 0.5% renders storage unattractive. The possibility of capturing CO2 from the air, not only from flue gases, makes storage with higher leakage rates interesting. Finally, we speculate about the role of imperfect carbon storage in carbon accounting and trading.