There is great potential for reducing greenhouse gas emissions (GHGE) from public sector meals. This paper aimed to develop a strategy for reducing GHGE in the Swedish school food supply without compromising nutritional adequacy, affordability, and cultural acceptability. Amounts, prices and GHGE-values for all foods and drinks supplied to three schools over one year were gathered. The amounts were optimized by linear programming. Four nutritionally adequate 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; Model 3 additionally constrained RD for individual foods to an upper and lower limit; and Model 4 further controlled how ratios between food groups could deviate. Models 1 and 2 reduced GHGE by up to 95% but omitted entire food categories or increased the supply of some individual foods by more than 800% and were deemed unfeasible. Model 3 reduced GHGE by up to 60%, excluded no foods, avoided high RDs of individual foods, but resulted in large changes in food group ratios. Model 4 limited changes in food group ratios but resulted in a higher number of foods deviating from the observed supply and limited the potential of reducing GHGE. Cost was reduced in almost all solutions. An omnivorous, nutritionally adequate, and affordable school food supply, with considerably lower GHGE is achievable with moderate changes to the observed food supply. Trade-offs will always have to be made between achieving GHGE reductions and preserving similarity to the current supply.