According to the most widely accepted Cattell–Horn–Carroll (CHC) model of intelligence measurement, each subtest score of the Wechsler Intelligence Scale for Adults (3rd ed.; WAIS–III) should reflect both 1st- and 2nd-order factors (i.e., 4 or 5 broad abilities and 1 general factor). To disentangle the contribution of each factor, we applied a Schmid–Leiman orthogonalization transformation (SLT) to the standardization data published in the French technical manual for the WAIS–III. Results showed that the general factor accounted for 63% of the common variance and that the specific contributions of the 1st-order factors were weak (4.7%–15.9%). We also addressed this issue by using confirmatory factor analysis. Results indicated that the bifactor model (with 1st-order group and general factors) better fit the data than did the traditional higher order structure. Models based on the CHC framework were also tested. Results indicated that a higher order CHC model showed a better fit than did the classical 4-factor model; however, the WAIS bifactor structure was the most adequate. We recommend that users do not discount the Full Scale IQ when interpreting the index scores of the WAIS–III because the general factor accounts for the bulk of the common variance in the French WAIS–III. The 4 index scores cannot be considered to reflect only broad ability because they include a strong contribution of the general factor.