  We describe a one-parameter family of dispersing (hence hyperbolic, ergodic
and mixing) billiards where the correlation function of the collision map
decays as $1/n^a$ (here $n$ denotes the discrete time), in which the degree $a
\in (1, \infty)$ changes continuously with the parameter of the family,
$\beta$. We also derive an explicit relation between the degree $a$ and the
family parameter $\beta$.
