We develop a 2-period emission trading model for a stock pollutant with demand shocks resolving over time. We find precise conditions for efficiency of a stabilization mechanism where cumulative available permits decrease with excess supply in early periods. Our model describes the stabilization rule, and identifies optimal parameters. The market stability mechanism substantially increases welfare, increases the domain of parameter values where (Stabilized) Banking outperforms Prices, and reduces price volatility. Our findings are important for emission trading schemes worldwide, such as California's Global Warming Solutions Act Scoping Plan, the U.S. Regional Greenhouse Gas Initiative, EU-ETS, and China's National ETS, the world’s largest carbon market.