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 rigorous and agreed definition of ZEB is yet to come. A parallel paper in this conference explains how a formal and comprehensive ZEB definition can be based on the evaluation of certain criteria. These criteria are extensively discussed in ongoing projects, both in Norway and internationally. The objective of this paper is to focus 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.