Several methods have been proposed to use the cycle consistency condition to improve the accuracy of free energy estimates. They could be classified into two types. The first type computes the free energies on edges of a cycle independently and then adjusts them to satisfy the cycle consistency condition. Such methods include the cycle closure correction (CCC) method and its weighted variant. The second type couples the calculations of free energies on edges of a cycle and estimate them simultaneously. An example method of this type is the MBARnet 11 method, which computes free energies on edges of a cycle by optimizing an objective function subject to the cycle consistency condition. Although there is little evidence suggesting which type of methods is more accurate, the second type can potentially make better use of the cycle consistency condition because it uses the condition throughout the calculation.