Custom Fields for Media items

I want to add something like ‘Custom Fields’ directly to Media items (images). Not tags, but fields to be filled in for every item. I would have thought that it would be simple, as the Media items are just types of Post and Page, but it seems strangely complicated.

I have also looked at register_setting() and add_setting_*() functions, but without some context (a full example) I can’t get my head around the docs.

Can’t find any pluings that do what I want either.

Any suggestions or help?