In this paper, we investigate the best delay LS inverse filter design problem. We propose FIR-IIR LS inverse filters to improve the LS error performance for the same complexity. Furthermore we present a new approach for the design of FIR-IIR LS inverse filters by using a special selection procedure for the IIR part. We derived the closed form LS error expressions and compared with the practical results in order to effectively show the performance improvement in this case. In general 4-5 dB improvement is achieved compared to the best delay LS inverse filter design approach.