Energy poverty is a multidimensional and continuously growing societal problem, with political roots. In pursuit of mitigating the problem, the European Commission has adopted a bundle of policies, such as consumer protection measures, short-term financial interventions, motivations for energy efficiency (e.g., energy retrofits and replacement of old household appliance) and information campaigns, among others. There is no doubt, however, that increasing the income of vulnerable households would be the most preferred and effective option. Focusing on energy efficiency, a measure typically incorporated in the National Energy and Climate Plans (NECPs) of many Member States as a means to fight energy poverty, this paper aims to shed light on the need to gradually move towards more localized—not to say personalized—actions. In this direction, a labeled choice-based experiment is used, which involves a hypothetical selection between three alternative energy interventions, i.e., house retrofit, upgrading of heating system and upgrading of household electrical appliances. The research aims to integrate the preferences of households from the choice experiment with indicators of energy poverty and establish a connection between energy poverty and energy efficiency investment decisions. The results demonstrate that households’ preferences are affected by qualitative and quantitative aspects of energy vulnerability and sociodemographic characteristics. Furthermore, vulnerable households seem to be more prone to the so-called “discounting gap”, as previous studies also suggest. These findings are worrisome because, without tailor-made support, these households may never escape the vicious circle of energy poverty. To this end, the survey could provide useful information to policy-makers towards developing more robust policies of energy poverty alleviation.