  Stochastic acceleration of $^3$He and $^4$He from a thermal background by
parallel propagating turbulent plasma waves with a single power-law spectrum of
the wavenumber is studied. In the model, both ions interact with several
resonant modes. When one of these modes dominates, the acceleration rate is
reduced considerably. At low energies, this happens for $^4$He, but not for
$^3$He where contributions from the two stronger modes are comparable so that
acceleration of $^3$He is very efficient. As a result, the acceleration of
$^4$He is suppressed by a barrier below $\sim 100$ keV nucleon$^{-1}$ and there
is a prominent quasi-thermal component in the $^4$He spectra, while almost all
the injected $^3$He ions are accelerated to high energies. This accounts for
the large enrichment of $^3$He at high energies observed in impulsive solar
energetic particle events. With reasonable plasma parameters this also provides
a good fit to the spectra of both ions. Beyond $\sim 1$ MeV nucleon$^{-1}$, the
spectrum of $^3$He is softer than that of $^4$He, which is consistent with the
observed decrease of the $^3$He to $^4$He ratio with energy. This study also
indicates that the acceleration, Coulomb losses and diffusive escape of the
particles from the acceleration site {\it all} play important roles in shaping
the ion spectra. This can explain the varied spectral shapes observed recently
by the {\it Advanced Composition Explorer}.
