This paper examines the impact of intercohort changes in social background composition on changes in grade progression rates at selected schooling levels. It is argued that the relative and absolute effects of background composition on grade progression rates should decline over levels of schooling. Empirical support for these arguments is offered, using data for white males born between 1907 and 1951. Whereas twentieth century increases in average educational attainment are primarily due to increases in grade progression rates at the elementary and secondary levels, future growth must occur through increases in transition rates beyond high school, given the near universality of high school graduation for cohorts born at midcentury. Analysis shows that postsecondary progression rates are much less responsive to changes in family background composition than rates earlier in the schooling process. Despite intercohort changes in background composition that are increasingly favorable to educational attainment, future educational growth may be slower than past growth because compositional effects on average attainment will be through progression rates where the effects are weak. (Author/GC)