Minimizing greenhouse gas emissions (GHGE) from public sector meals harbours considerable potential to reduce climate impact. This paper aimed at finding the best possible strategy for reducing GHGE in the Swedish school food supply without compromising its nutritional adequacy, affordability, and cultural acceptability. Prices, amounts, and GHGE of all foods and drinks supplied to three schools over one year were optimized by linear programming. Three models were developed: Model 1 minimized GHGE while constraining relative deviation (RD) from observed food supply; Model 2 minimized total RD while imposing stepwise GHGE reductions; and Model 3 additionally constrained RD to -75% and +200% of the observed value. Model 1 reduced GHGE by 89-95% with an average RD (ARD) from observed food supply of 480-887%. In Model 2, comparable GHGE reductions (80%-95%) at lower ARD (78%-459%) were achieved but with high RDs for individual foods. Model 3 excluded no foods, avoided high RDs, and reduced GHGE by 40% in all schools with ARDs of 7.2-8.1% at 12-15% lower cost. An omnivorous, nutritionally adequate, and affordable school food supply with considerably lower GHGE is achievable with moderate changes to the observed food supply. This method can also be applied in other settings and countries.