A classic version of convergence theory was proposed by Marion Levy (1966) as part of his theory of modernization: if and as the level of modernization increases (defined as a higher ratio of reliance upon inanimate energy and tools, relative to animate energy), the level of structural uniformity among relatively modernized societies continually increases. This hypothesis that there is more uniformity among modernized than among non-modernized societies is tested here with cross-national data from 148 non-modernized and 52 modernized societies. Using the coefficient of variation (V) as the measure of convergence, I analyze a wide range of variables: level of economic development, capitalist market economy, demographic variables, technology, the state and political democracy, cognitive modernization, health, income inequality and poverty, gender particularism-universalism, and information and communications. I find that the modernized societies do show more convergence (lower V scores) than the non-modernized societies on 49 of the 51 variables tested. Among the 21 societies that were already modernized in 1965, as they became more modernized during the period from1965 to the present, they also became more convergent on 32 of the 45 variables analyzed. Thus, variation in social structure is greater among less modernized than among more modernized societies, and this has implications for theories of globalization.