Tariff indexes such as trade weighted means, variances and coefficients of variation are commonly used to compare the overall restrictiveness of trade policy over time and across countries despite their lack of theoretical foundation. Anderson and Neary (1991) define a welfare-consistent tariff index, the trade restrictiveness index. This paper compares the various concepts and shows how the trade restrictiveness index may be expressed in terms of "marginal trade weighted moments" of the tariff schedule. In the Cobb-Douglas case, the trade restrictiveness index collapses to a function of a trade-weighted variance of tariffs are efficient.