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.
(..) a better place for it. I'm gonna take one last look... and then I'm gonna put it where it belongs. Gwen's speech. It is easy to feel hopeful on a beautiful day like today. But there will be dark days ahead of us too. There will be days when you feel all alone and that's when hope is needed most. (..)2014 The Amazing Spider-Man 2