In one illustrative example, a spin valve (SV) sensor of the self-pinned type includes a free layer; an antiparallel (AP) self-pinned layer structure; and a non-magnetic electrically conductive spacer layer in between the free layer and the AP self-pinned layer structure. The AP self-pinned layer structure includes a first AP pinned layer having a first thickness; a second AP pinned layer having a second thickness; and an antiparallel coupling (APC) layer formed between the first and the second AP pinned layers. The first thickness is slightly greater than the second thickness. Configured as such, the AP pinned layer structure provides for a net magnetic moment that is in the same direction as a magnetic field produced by the sense current flow, which reduces the likelihood of amplitude flip in the SV sensor.