A current-perpendicular-to-the-plane (CPP) magnetoresistive sensor has an antiparallel free (APF) structure as the free layer and a specific direction for the applied bias or sense current. The (APF) structure has a first free ferromagnetic (FL1), a second free ferromagnetic layer (FL2), and an antiparallel (AP) coupling (APC) layer that couples FL1 and FL2 together antiferromagnetically with the result that FL1 and FL2 have substantially antiparallel magnetization directions and rotate together in the presence of a magnetic field. The thickness of FL1 is preferably greater than the spin-diffusion length of the electrons in the FL1 material. The minimum thickness for FL2 is a thickness resulting in a FL2 magnetic moment equivalent to at least 10 Å Ni80Fe20 and preferably to at least 15 Å Ni80Fe20. The CPP sensor operates specifically with the conventional sense current (opposite the electron current) directed from the pinned ferromagnetic layer to the APF structure, which results in suppression of current-induced noise.