A magnetic recording system uses a magnetic recording medium having a laminated magnetic structure with at least three magnetic layers, wherein the magnetic layers have decreasing intrinsic coercivity H.sub.0 with distance from the write head. The write field at the center of each magnetic layer is greater than that layer's H.sub.0. The magnetic layers have different compositions and/or thicknesses and thereby different values of H.sub.0. The alloys used in the middle and upper magnetic layers are relatively "high-moment" alloys that would not ordinarily be used in magnetic recording media because they have relatively low S.sub.0NR, but the overall S.sub.0NR of the laminated magnetic structure is improved because of the effect of lamination. The middle and upper magnetic layers can be made substantially thinner, which enables the magnetic layers to be located closer to the write head, thereby exposing each of the magnetic layers to a higher write field.