We inserted NiFe/CoFe/antiferromagnetic-MnIr/CoFe layers between two CoTaZr soft layers to enhance the exchange-bias field (Heb) and then evaluated the effect of this lamination on the spike noise and recording characteristics of CoCrPt-SiOx media with an exchange-biased soft magnetic underlayer (SUL). The two CoTaZr layers were exchange-biased radially throughout the disk, and a higher Heb was obtained for the upper CoTaZr layer. By using the laminated SUL, spike noise was suppressed even when the total thickness of the CoTaZr layers was increased to 300 nm. Although the medium had a high Hc of 7.0 kOe, a fairly good overwrite and signal-to-noise ratio were obtained. As another application of exchange biasing, we also examined the possibility of combining exchange biasing and antiparallel-coupled (APC) soft layers; i.e., a pinned APC SUL. An exchange-bias field from the pinning layers to the lower CoTaZr layer and an exchange-coupled field between the two CoTaZr layers were successfully applied. The medium with the pinned APC SUL showed no spike noise throughout the disk, and wide-area adjacent track erasure was effectively suppressed.