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Offsets lower the cost of cap-and-trade programs but must be considered imperfect if they cannot exclude “non-additional” emissions reductions or sequestration gains that would have occurred in their absence. Non-additionality can be addressed by requiring project-level additionality tests, by adjusting the mandatory emissions cap, or by imposing a trading ratio requirement on offset credits. Additionality tests most completely put the welfare impact on non-additional abaters but are challenging to implement. A cap adjustment is simple but places the entire welfare impact on the capped sector. A trading ratio, also simple, spreads the welfare impact across the capped and uncapped sectors. A trading ratio may either increase or decrease the welfare of the uncapped sector. When the quantity of non-additional abatement is uncertain, a cap adjustment has lower aggregate costs than a trading ratio, whereas a trading ratio has less variance with respect to quantity of emissions reduced.