  This paper studies variance functions of Cauchy-Stieltjes Kernel families
generated by compactly supported centered probability measures. We describe
several operations that allow us to construct additional variance functions
from known ones. We construct a class of examples which exhausts all cubic
variance functions, and provide examples of polynomial variance functions of
arbitrary degree. We also relate Cauchy-Stieltjes Kernel families with
polynomial variance functions to generalized orthogonality.
  Our main results are stated solely in terms of classical probability; some
proofs rely on analytic machinery of free probability.
