We use Mixed-Complementarity-Problem programming to implement tariff rate quotas (TRQ) in the global CGE LINKAGE model. We apply the approach to tariff rate quotas in sugar markets in OECD countries. We calibrate the model on 2000 policy levels for OECD countries to reflect the full implementation of their World Trade Organization commitments. We look at reforms of TRQ and TRQ-like schemes in the EU, the United States, and Japan, as well as multilateral trade liberalization. We derive the impact of reforms on welfare, bilateral trade flows, and terms of trade. A 33-percent multilateral decrease of ad-valorem tariffs, combined with a 33-percent increase in imports under TRQ-like schemes in the EU, the United States, and Japan, induces a global welfare gain of about 889 million dollars. These three countries' trade policies create substantial trade diversion, which excludes many low-cost producers from trading opportunities. An expansion of their import quotas alone, without multilateral trade liberalization, induces welfare gains but preserves most of the trade diversion patterns. The latter diversion benefits some Least Developed Countries' producers because of granted bilateral TRQ allocations. In the context of greater market access, reductions in tariffs in the EU and the United States, and in border "surcharges" in Japan will have to be dramatic before they can significantly affect trade flows as compared to TRQ expansion. Full multilateral trade liberalization induces global welfare gains of about $3 billion.