The various assessments of the effects of a liberalization of world sugar markets are largely inconsistent. One cause seems to be the modeling of the EU supply response. We investigate three possible linkages between production quota sugar and the out-of-quota or "C" sugar supply: i/ the existence of fixed costs covered by the in-quota sugar; ii /the "overshooting" behavior as prevention against poor yields; iii/ the production of C sugar as "reference building" in view of expected reforms. Modeling these effects results in the introduction of an implicit cross-subsidy between in quota sugar and C sugar. The resulting specification is included in a detailed model of EU agricultural sector so as to account for intersectoral linkages. We simulate the effects of the reform of the sugar sector proposed by the EU Commission in July 2004 and the effects of a ban on sugar export subsidies. The cuts in production and prices required to eliminate export subsidies are larger than those proposed by the Commission. However, the reform proposal makes large a decrease in tariffs possible. The need to eliminate export subsidies appears more constraining than the constraints on tariffs reduction for the EU. As expected, different assumptions on the interaction between in-quota prices and C sugar supply have a significant impact on the results and explain some of the differences observed in the literature regarding the effect of sugar market liberalization.