Current and proposed greenhouse gas cap-and-trade systems allow regulated entities to offset abatement requirements by paying unregulated entities to abate. These offsets from unregulated entities are believed to contain system costs and stabilize allowance prices. However, the supply of offsets is highly uncertain. Furthermore, the offset supply uncertainty may be correlated with other sources of uncertainty in emissions trading systems. This paper presents a model that incorporates both uncertainties in the supply of offsets and in abatement costs. Using numerical methods we solve the model under a variety of parameter settings, including a system that includes allowance price controls. We find that as uncertainty in offsets and uncertainty in abatement costs become more negatively correlated, expected abatement plus offset purchase costs increase, as does the variability in allowance prices and emissions from the regulated sector. Imposing an allowance price collar that limits the upper and lower cost substantially mitigates cost increases as well as the variability in prices and emissions, while roughly maintaining expected environmental outcomes.