A technique for designing IIR (infinite impulse response) filters to simultaneously meet arbitrary magnitude and group delay specifications, without explicit equalizer sections, through the use of balanced model reduction is described. FIR (finite impulse response) design tools which make the approximation task relatively easy are employed prior to an FIR-to-IIR conversion process. The use of this reduction algorithm in a real-time FIR system identification and subsequent IIR compensation scene is also reported.>