  We employ a functional renormalization group to study interfaces in the
presence of a pinning potential in $d=4-\epsilon$ dimensions. In contrast to a
previous approach [D.S. Fisher, Phys. Rev. Lett. {\bf 56}, 1964 (1986)] we use
a soft-cutoff scheme. With the method developed here we confirm the value of
the roughness exponent $\zeta \approx 0.2083 \epsilon$ in order $\epsilon$.
Going beyond previous work, we demonstrate that this exponent is universal. In
addition, we analyze the generation of higher cumulants in the disorder
distribution and the role of temperature as a dangerously irrelevant variable.
