Energy is one of essential productive resources in economic activities and its efficiency improvement is taken one of the key measures for energy conservation to promote economic growth as well as reduce air pollution. Several large energy consumption regions such as China, India, and Europe have set targets on lowering energy intensity - physical energy use per unit economic output - widely accepted as an indicator of energy efficiency. One percent reduction in energy intensity is expected to conserve one percent physical energy use from an engineer’s perspective. However, the reduction in energy intensity would probably stimulate economic growth and result in more “unexpected” energy use, namely rebound effect on energy use. To convey the rebound effect consequences to policy makers, business managers, engineers, researchers and other stakeholders who take energy intensity an indicator of energy efficiency and a measure for energy conservation, the present article offers a method starting from a general form of production function to identify properties of and analyze key drivers behind the rebound effect. Different from the strict definition of rebound effect in energy economics, where energy efficiency is narrowly defined as energy-augmented or energy-specific technological change, measurable partial rebound effect of energy intensity reduction would be the most preferred output for a policy maker who pursues targets of both economic growth and energy conservation. We have also presented empirical results for 40 regions for illustration.