The disturbance decoupling problem by state feedback (DDP) is solved for a class of linear systems where the left-invertible systems are included. Also obtained is a complete characterization of the solution as well as the parameterization of all corresponding state feedback matrices. Such characterization enables one to conclude about the solvability of DDP with stability and/or pole placement. A numerical method is proposed for computation of the controllers in an analytical form, suitable to the treatment of complementary design specifications. The solution of the disturbance decoupling problem by measurement feedback (DDPM) is also discussed and, based on the results obtained for DDP, a procedure for design of a reduced-order compensator is proposed.