Energy refurbishments of buildings can substantially contribute to economy-wide energy efficiency improvements, leading to decarbonisation and additional sustainability benefits. Prioritising the most economically promising investments is not straightforward because apart from cost-effectiveness calculations, several real-world constraints have to be taken into account. This paper describes an approach to assess the economically viable energy efficiency potential in the building sector of the Mediterranean island of Cyprus, with a combination of detailed engineering modelling, cost-effectiveness calculations and real-world considerations of budgetary, technical, behavioural and market constraints. We examine diverse cost-effectiveness indices and come up with a proposal for prioritising specific energy investments such as the installation of heat pumps, insulation of roofs, and replacement of lighting and electronic equipment-without however ignoring other measures that may be economically less favourable but can realistically be implemented in a limited number of buildings. Finally we address the governance of energy efficiency policies, focusing on weaknesses of the current regulatory environment in Cyprus, which can be generalised for many other countries facing similar dilemmas.