  For $\,0<\alpha\le \infty$, new subclasses $\,\mathcal{U}^{<\alpha>}$ of the
class $\,\mathcal{U}$, of s-selfdecomposable probability measures, are studied.
They are described by random integrals, by their characteristic functions and
their L\'evy spectral measures. Also their relations with the classical L\'evy
class $L$ of selfdecomposable distributions are investigated.
