Otto used my model of the tight projective plane with one handle to construct tight immersions of \RP2 with two handles in every CES.

The idea is to remove the outer handle and use the central core as though it were a "handle" being added to a tight "tube" torus.

(Instead of adding the core to a sphere with two disks removed, it is added to a torus with two disks removed, so has one additional handle.)