  We review and extend the composite fermion theory for semiconductor quantum
dots in high magnetic fields. The mean-field model of composite fermions is
unsatisfactory for the qualitative physics at high angular momenta. Extensive
numerical calculations demonstrate that the microscopic CF theory, which
incorporates interactions between composite fermions, provides an excellent
qualitative and quantitative account of the quantum dot ground state down to
the largest angular momenta studied, and allows systematic improvements by
inclusion of mixing between composite fermion Landau levels (called $\Lambda$
levels).
