In this contribution we consider the effect of a class of ''averaging
operators'' on isotropic fitness landscapes. Explicit expressions for
the correlation function of the averaged landscapes are derived. A new
class of tunably rugged landscapes, obtained by iterated smoothing of
the random energy model, is established. The correlation structure of
certain landscapes, among them the Sherrington-Kirkpatrick model, rem
ains unchanged under the action of all averaging operators considered
here.