Dream Hunter Rem (1985)

Original title: ドリームハンターレム

Rem can't sleep - ever - but she can enter the world of dreams just the same, so she decides to use her unusual powers ti make a living as a private investigator in the dreamworld. Lieutenant Sakaki doesn't think it's a good idea... This is the original, 1-part hentai version of the OVA, later remade into a less-explicit version with 2 additional episodes.