This paper provides empirical evidence and theoretical grounds to support the existence of energy cost constants, i.e., relatively stable energy costs to income ratios, not only country-wide, but also in major energy end-use sectors. These ratios are similar across different countries at different stages of economic development, but they also depend on the country-specific economy structure and legacy of previous long-standing energy pricing, taxes, and subsidies policies, which it takes time to shift from. The aggregated country-wide energy costs constant (range) is a linear combination of those for sectors weighted by the contributions of respective sectors’ income indicators to either gross output or GDP. Deviation of energy costs shares from the constrained range is possible but limited. The “rule of gravitation” goes: for the whole cycle real energy prices in each sector may grow only as much as energy intensity declines, and inversely promoting energy efficiency can be viewed as a policy, of which the environmental cobenefits will be undermined by rebound effects, unless it is accompanied by rising energy prices.