  We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
  Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
  These developments are illustrated on the so-called radial sextic oscillator.
