This study has analysed which options would be appropriate to use as additional requirements to the main requirement of primary energy number in the new Swedish building regulations. The starting point is to ensure that buildings are built with good qualitative properties in terms of the building envelope so that low energy use can be maintained throughout the life of the building despite changes in installation systems or the building's occupancy. The additional requirements should aim to minimize energy losses, i.e., to ensure that the building's total energy demand is low. The following possible additional requirements have been examined: net energy demand, net energy demand for heating, heat power demand, heat loss rate and average heat transfer coefficient. In order to ensure that the additional requirements will work as desired and to explore possibilities with, and identify the consequences of, the various proposals, calculations have been made for four different categories of buildings: single-family houses, apartment buildings, schools and offices. The results show that the suggested option net energy demand will not contribute to any additional benefits in relation to primary energy number. The other options analysed have both advantages and disadvantages and it is difficult to find a single additional requirement that fulfils all the pre-set demands.