Tire pressure question

I am almost afraid to post this but have not seen any consideration regarding rim bead width to tire tread width. The decision to mount correct tire size to available rim comes first. I was always taught tire width should equal bead width as a point of reference. Yes you can deviate from this and by how much I don't know but have seen too wide of tire on too narrow of a rim. Is it possible to correct for proper wear by adjusting pressure in this situation?
I actually have both situations for one car.
I have a 315/60x15 drag radials, recommended for a 8.5-11 rim on a twelve. I have seen them on a fourteen. They work best on a wider rim (11.5 tread width)
The street tires I have for the same car, are too wide for the rim. They have 15+inches of tread, on a twelve inch rim. They are run fairly soft, under 20 lbs, to avoid wearing out the center. They will still have plenty of excess load rating, it's a light car.