This paper provides important new insights into the reasons for the observed gap in educational attainment between children of immigrants and natives in Denmark using a dynamic discrete model of educational choices to determine at what stages of their educational careers children of immigrants face barriers to educational progression and how background characteristics affect educational choices at different points in the educational system. The main findings of the paper are that dropout rates from vocational upper secondary education are much higher among children of immigrants and that strengthening family characteristics reduces the dropout rates. However, behavioral differences and/or differences in constraints and institutional factors are also important barriers and thus determinants of the observed educational gaps as is age at immigration. (Contains 9 tables.)