  Properly regularized second-order degenerate perturbation theory is applied
to compute the contribution of higher Landau levels to the low-energy spectrum
of interacting electrons in a disk-shaped quantum dot. At ``filling factor''
near 1/2, this contribution proves to be larger than energy differences between
states with different spin polarizations. After checking convergence of the
method in small systems, we show results for a 12-electron quantum dot, a
system which is hardly tractable by means of exact diagonalization techniques.
