The polynomial matrix equation $X_lD_r$ $+$ $Y_lN_r$ $=$ $D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^{-1}Y_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function $N_rD_r^{-1}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by $D_k$. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.