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Buildings are responsible for a large portion of global greenhouse gas emissions. While energy efficiency features can significantly reduce the greenhouse gas emissions during a building's operational stage, extra materials and processes associated with these features typically involve higher greenhouse gas emissions during the construction phase. In order to study this relationship, a case study of a highly energy-efficient house in rural Alaska was performed. For the purposes of this case study, a theoretical counterpart home was designed that has the same interior space, but insulation values close to the code minimum requirements. Using computer simulations, a Life Cycle Assessment (LCA) was performed for the case study home as well as its conventional counterpart. The extra greenhouse gas emissions associated with the construction of the case study home were compared to the annual savings in greenhouse gas emissions achieved thanks to the energy efficiency features, and carbon payback was calculated. The carbon payback was calculated to be just over three years, which is only a small fraction of the life of the building. The results of this study show that despite higher greenhouse gas emissions during the construction phase, highly energy-efficient homes can play an important role in addressing climate change.