  We use the numerical renormalization group method to study an Anderson
impurity in a conduction band with the density of states varying as rho(omega)
\propto |omega|^r with r>0. We find two different fixed points: a local-moment
fixed point with the impurity effectively decoupled from the band and a
strong-coupling fixed point with a partially screened impurity spin. The
specific heat and the spin-susceptibility show powerlaw behaviour with
different exponents in strong-coupling and local-moment regime. We also
calculate the impurity spectral function which diverges (vanishes) with
|omega|^{-r} (|\omega|^r) in the strong-coupling (local moment) regime.
