Measurement of energy poverty has been a missing priority in energy research. There is hardly any consensus regarding whether to consider energy as a resource or capacity, output or outcome, and quantity or service. In this paper, we revisit major approaches in literature to assess energy poverty: economic, engineering, and access-based, including others. We critique the economic and engineering approaches for the arbitrariness of cut-offs and the misplaced emphasis on less meaningful energy quantity. Finding the access-based approach most suitable, we propose a method of assessing energy poverty based on deprivation in modern cooking and lighting fuels. We divide the energy-poor into three groups: transitional, moderate, and extreme energy-poor. We apply the method to India's urban areas of different states and union territories using the national sample survey data. The results reveal energy poverty to be primarily dictated by deprivation in cooking and a greater incidence of energy poverty in larger states. In contrast to conventional measures, we compute the depth and severity of energy poverty only for energy-poor as opposed to for the entire population. These complementary measures depict energy poverty of energy-poor more accurately and therefore will direct the attention of pro-poor energy policies and programmes appropriately.