The International Comparisons Program (ICP) compares the purchasing power of currencies and real income across countries. ICP is broken up into six regions. Global results are then obtained by linking these regions together at both basic heading level and the aggregate level in a way that satisfies within-region fixity (i.e., the relative parities of a pair of countries in the same region are the same in the global comparison as in the within-region comparison). Standard multilateral methods violate this within-region fixity requirement and hence cannot be used to construct the global results. A method is proposed here that resolves this problem by altering the price and quantity indexes by the least-squares amount necessary to ensure that within-region fixity is satisfied. This method is then compared–both in terms of its underlying structure and empirically–with other methods for imposing within-region fixity.