  We confirm the Kosterlitz-Thouless scenario of the roughening transition for
three different Solid-On-Solid models: the Discrete Gaussian model, the
Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with
standard (cosine) action. The method is based on a matching of the
renormalization group flow of the candidate models with the flow of a bona fide
KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are
performed using efficient cluster algorithms. We obtain high precision
estimates for the critical couplings and other non-universal quantities. For
the XY model with cosine action our critical coupling estimate is
$\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian
and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and
$K_R^{ASOS}=0.8061(3)$, respectively.
