  We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts
$(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t -
\tau_t$ belongs to a certain Schatten-von Neumann class $\gS_p$ with $p\ge 1$.
We show that, for the unitary component in the Wold-Kolmogorov decomposition of
the cogenerator of the semigroup $(\tilde\tau_t)_{t\ge 0}$, {\it any singular}
spectral type may be achieved by $\gS_1$ perturbations. We provide an explicit
construction for a perturbation with a given spectral type based on the theory
of model spaces of the Hardy space $H^2$. Also we show that we may obtain {\it
any} prescribed spectral type for the unitary component of the perturbed
semigroup by a perturbation from the class $\gS_p$ with $p>1$.
