In my opinion it depends on how related the modules are and how they are 'use'd. When you say 'thingy', I assume you mean module/object. If Foo::Bar uses uses Quux for implementing certain methods Foo::Bar without any inheritance, then you could have Foo::Bar::Quux.
However, if Foo::Bar are related as in they both apply to Foo but not directly to each other, they I would suggest using Foo::Quux. (OT: anyone know how to pronounce quux?)
Foo::Bar new(-Quux): I don't like this because it appears that quux is separate from bar and should therefore be in a separate module altogether.
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