  The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving
deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be
considered as a family of commuting time-dependent Hamiltonian systems on the
direct product of $n$ copies of $m\times m$ matrix algebras equipped with the
standard linear Poisson bracket. In this paper we address the problem of
reduction of particular solutions of ``more complicated'' Schlesinger equations
$S_{(n,m)}$ to ``simpler'' $S_{(n',m')}$ having $n'< n$ or $m' < m$.
