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Energies are reported for the first four singlet and triplet spherically symmetric states of 2
e
systems confined in an impenetrable sphere. All calculations used explicitly correlated Hylleraas basis sets. These calculations identify a series of level crossings and avoided crossings for Coulombic systems with a positive charge at the center of the sphere. Similar crossings do not occur for the 2
e
quantum dot. Configuration interaction calculations conducted in parallel provide a description of the system within the more traditional atomic orbital picture. The general shape of the energy versus confinement graphs and the locations of level crossings are shown to be consequences of scaling properties of the interparticle potentials.