In this paper, we assess the extent to which redistributive trends within Social Security are affected when the Old Age and Survivors Insurance (OASI) program is converted to an OASDI program through the addition of Disability Insurance (DI). Our analysis covers four cohorts spanning 1931-1964, using a preliminary version of the jointly developed Modeling Income in the Near Term (MINT) model, version 3. We present detailed measures of redistribution - before and after accounting for Disability Insurance - based on beneficiaries' "own," "received," and "shared" benefits and broken out by gender, race, educational attainment, and lifetime earnings quintile. We then use these measures to comment on the amount of redistribution and progressivity the DI program introduces into the system and the extent to which various groups do or do not benefit.