Conceptually a Zero Emission Building (ZEB) is a building with greatly reduced energy demand and able to generate electricity (or other carriers) from renewable sources in order to achieve a carbon neutral balance. However, a clear and agreed definition of Zero Emission Building (ZEB) is yet to be achieved, both internationally and in Norway. However, it is understood that both the definition and the surrounding energy supply system will affect significantly the way buildings are designed to achieve the ZEB goal. A formal definition of ZEB is characterized by a set of criteria that are: the system boundary, feeding-in possibilities, balance object, balancing period, credits, crediting method, energy performance and mismatch factors. For each criterion different options are available, and the choice of which options are more appropriate to define ZEBs may depend on the political targets laying behind the promotion of ZEBs, hence may vary from country to country. This paper focuses on two of these criteria: energy performance and credits used to measure the ZEB balance. For each criterion different options are considered and the implications they have on the building design are assessed. The case study is on a typical Norwegian single family house. It is shown that for certain choices on the two criteria options, a paradoxical situation could arise. When using off-site generation based on biomass/biofuels, achieving the ZEB balance may be easier for high energy consuming buildings than for efficient ones. This is the exact opposite of what ZEBs are meant to promote: design of energy efficient buildings with on-site generation options. Recommendations on how to avoid such a paradox are suggested.