A current-perpendicular-to-the-plane spin-valve (CPP-SV) magnetoresistive sensor has a high-resistivity amorphous ferromagnetic alloy in the free layer and/or the pinned layer. The sensor may have an antiparallel (AP)-pinned structure, in which case the AP2 layer may be formed of the high-resistivity amorphous ferromagnetic alloy. The amorphous alloy is an alloy of one or more elements selected from Co, Fe and Ni, and at least one nonmagnetic element X. The additive element or elements is present in an amount that renders the otherwise crystalline alloy amorphous and thus substantially increases the electrical resistivity of the layer. As a result the resistance of the active region of the sensor is increased. The amount of additive element or elements is chosen to be sufficient to render the alloy amorphous but not high enough to substantially reduce the magnetic moment M or bulk electron scattering parameter .beta..