Al~tract--ln Sweden, Combined generation of Heat and Power (CHP) is in common practice. Different fuels are burnt in a boiler and the steam is used for generating electricity. The heat that has to be transferred from the condenser in the plant is used in the district heating grid. This grid is thus used as a cooling facility necessary for electricity production. However, energy conservation in the Swedish building stock is also encouraged, and if this is utilized in district heated buildings it results in fewer possibilities for electricity production. This might be a major drawback when nuclear power is abolished, as is the result from a consensus some years ago. This paper deals with the question of whether it is better to conserve both heat and electricity, to save only one of the energy forms or if it is cheaper to produce more energy, instead of saving. A case study is presented dealing with Maim6, in the South of Sweden, and it is shown that energy conservation in district heated buildings cannot yield profitability: neither can conservation in the electricity grid, even if it gets closer to profitable savings. It is assumed that the total cost of heating, insulation and electricity is paid by the society and the minimum point for this cost will characterize the best solution.