It can be argued that one way to reduce the dependence from external energy sources, is simply to reduce the demand for energy. Energy savings may thus be considered a policy priority when concerns for energy security are particularly strong. Drawing on an original econometric approach, we check whether policies and measures that affect indicators of energy efficiency performance have an analogous effect on security of supply indicators, both at the whole economy level and within the main sectors of energy use in the EU 15 countries and Norway. Our analyses show that the indicators studied are affected by a number of policies and measures; however very few of them seem able to tackle effectively and simultaneously, energy efficiency, carbon efficiency and energy security. The main lesson to be drawn from this analysis is therefore that there is a number of energy efficiency policies in the EU that do work, but there is no silver bullet able to successfully address different policy objectives. Taking a more general perspective, what seems to work is the policy mix rather than this or that policy in insulation.