Using one boolean object for two adjacent objects

Hey guys,
I’m trying to figure out how to get a clean mesh after applying a boolean modifier using a tangent object.
The only solution I found so far is to use separate, slightly larger boolean objects, otherwise a ring shown on below screenshot always remains.
Are there any other possibilities for such use case: two adjacent objects with holes of different diameter?
bool1 bool2

boolean_solution.blend (628.9 KB)