Sheaf terminology question

Given a coverage on a small category, the condition for a Set-valued presheaf on the category to be a sheaf has an existence part and a uniqueness part. If only the uniqueness part holds, one says that the presheaf is separated. Is there a name out there for presheaves that only satisfy the existence part of the sheaf condition? Andy Pitts [For admin and other information see: http://www.mta.ca/~cat-dist/ ]