A general procedure is presented to construct conditionally exactly solvabl
e (CES) potentials using the techniques of supersymmetric quantum mechanics
. The method is illustrated with potentials related to the harmonic oscilla
tor problem. Besides recovering known results, new CES potentials are also
obtained within the framework of this general approach. The conditions unde
r which this method leads to CES potentials are also discussed. (C) 1999 Pu
blished by Elsevier Science B.V. All rights reserved.