  We investigate trace formulas for one-dimensional Schroedinger operators
which are trace class perturbations of quasi-periodic finite-gap operators
using Krein's spectral shift theory. In particular, we establish the conserved
quantities for the solutions of the Korteweg-de Vries hierarchy in this class
and relate them to the reflection coefficients via Abelian integrals on the
underlying hyperelliptic Riemann surface.
