  Using the exactly solvable excitation spectrum of two-electron quantum dots
with parabolic potential, we show that the inclusion of the vertical extension
of the quantum dot provides a consistent description of the experimental
findings of Nishi et al. [Phys.Rev.B75, 121301(R) (2007)]. We found that the
second singlet-triplet transition in the ground state is a vanishing function
of the lateral confinement in the three-dimensional case, while it always
persists in the two-dimensional case. We show that a slight decrease of the
lateral confinement leads to a formation of the Wigner molecule at low magnetic
fields.
