Otto conjectures that no smooth tight immersions of $\RP2$ with two handles
exist in any CES, and that no tight immersion (smooth or polyhedral) of
$\RP2$ with one handle exists in any CES.
It turns out that both these conjectures are false.
Indeed there exist tight embeddings of $\RP2$ with one handle in several CES, and immersions in all the others except one.
This gives us smooth tight embeddings or immersions of $\RP2$ with two handles in all CES but one, by the usual addition of handles.
As it happens, the final CES also allows a smooth immersion of this surface.