  Paramagnetic, dipolar Hund's case-a radicals are considered in the presence
of arbitrary, non-collinear combinations of electric and magnetic fields. The
field-dependent part of the Hamiltonian is found to be exactly diagonalizable,
and described by quantum numbers given by the projection of the molecule's
total angular momentum along a space-fixed axis that is determined by both the
fields and the electric and magnetic dipole moments of the molecule. In cases
of strong fields, this procedure identifies a set of quantum numbers for the
molecule in crossed fields. We dub this set a "Hund's case-X" basis.
