Investigators report that there have been some 'hopeful' developments in the case.
a presidential 'hopeful' [=a person who hopes to become president]
There are 'hopeful' signs that the crisis may end soon.
(..) I know, right? What's going on, guys? Tell her, Gus. I wanted to attend my own funeral. I mean, I'm hopeful that I'll be able to attend as a ghost, but... (LAUGHING) However, just in case it doesn't work out... I decided to plan (..)2014 The Fault in Our Stars