FIR compensator design for H₂-optimal decoupling of measurable or previewed signals in discrete-time linear time-invariant systems is considered. The algorithm for the FIR system weighting matrices computation is based on pseudoinversion techniques aiming to minimize the l₂ norm of the overall system inpulse responses. The inherent dimensionality constraint of these techniques is overcome by welding problems referring to subsequent time subintervals of the FIR system window. The solution of the H₂-optimal state observation problem with unknown inputs straightforwardly comes by duality.