A robust carbon tax would generate considerable revenue. Some carbon tax advocates have suggested returning those revenues to Americans through direct payments, often called carbon dividends. We examine how to design these dividends considering two, sometimes conflicting, principles. Carbon dividends can be viewed as shared income from a communal property right, much as Alaskans share in income from the state’s oil resources. Dividends can also be viewed as rebating the carbon tax back to consumers. These views often have different implications for designing carbon dividends. Political and practical considerations are also important. With that in mind, we propose a carbon dividend design that combines beneficial features from both the communal property and tax rebate views.