  An exactly solvable model of the sawtooth chain with Ising and Heisenberg
bonds and with coupling to lattice distortion for Heisenberg bonds is
considered in the magnetic field. Using the direct transfer-matrix formalism an
exact description of the thermodynamic functions is obtained. The ground state
phase diagrams for all regions of parameters values containing phases
corresponding to the magnetization plateaus at $M=0,1/4$ and 1/2 have been
obtained. Exact formulas for bond distortions for various ground states are
presented. A novel mechanism of magnetization plateau stabilization
corresponding to $M=1/4$ state is reported.
