We explore possible low-GWP refrigerants by defining optimal thermodynamic properties and comparing those to properties estimated for a database of millions of compounds. We find that the optimal characteristics are quite rare; additional fluids are eliminated because they are unstable or toxic. We then estimate the cycle performance of the remaining candidates and apply efficiency as an additional screening criterion. The result is a handful of low-GWP candidates, and even these present tradeoffs. We argue that these represent all the viable candidates for single-component, medium- and high-pressure refrigerants—in other words, we have hit the limits of what chemistry allows.