Recent years have seen a rapid increase in the number of cap-and-trade schemes to mitigate greenhouse gas emissions. With many independently operating systems, policy discussions have turned to the topic of linking. This paper offers a theory of optimal linking. We show that an efficient linkage adjusts the joint cap in response to inter-scheme trades of allowances. Compared to standard linking, our proposal has two major advantages. First, it increases global welfare by efficiently adjusting the cap in response to private information implicitly contained in inter-scheme trades. Second, post-linking price volatility is lower with an endogenous cap. The latter advantage may alleviate existing political barriers to linking such as imported price volatility. A key concept in our analysis is asymmetric uncertainty. Interestingly, while asymmetric information generally decreases welfare, asymmetric uncertainty compensates for part (or, in extreme cases, all) of that welfare loss.