  In a recent paper Cari\~nena et al analyzed a non-polynomial one-dimensional
quantum potential representing an oscillator which they argued was intermediate
between the harmonic and isotonic oscillators. In particular they proved that
it is Schr\"odinger soluble, and explicitly obtained the wavefunctions and
energies of the bound states. In this paper we show that these results can be
obtained much more simply by noting that this potential is a supersymmetric
partner potential of the harmonic oscillator. We then use this observation to
generate an infinite set of potentials which can be exactly solved in a similar
manner.
