  A model of disordered spin-Peierls system is considered, where domain walls
are randomly distributed as a telegraph noise. For this realization of the
disorder in an XX spin chain, we calculate exactly the density of states as
well as several thermodynamic quantities. The resulting physical behavior
should be qualitatively unchanged even for an XXZ chain, up to the isotropic
XXX point. For weak disorder, besides a high energy regime where the behavior
of a pure spin-Peierls system is recovered, there is a cross-over to a low
energy regime with singular thermodynamic properties and enhanced
antiferromagnetic fluctuations. These regimes are analyzed with the help of
exact results, and the relevant energy scales determined. We discuss the
possible relevance of such a disorder realization to the doped inorganic
spin-Peierls compound CuGeO$_3$.
