I can't remember the whole rule of thumb, but in essence, within an inch for tire to rim width. If there is more sidewall, you can stretch the tire more, but not by much. Having a rim thinner than the tire will give a better ride, as the sidewall will flex more, but the rim float side to side inside the tire during turning.
The most I pushed was I ran a 33x12.50x15 on a 15x8 rim. When measured with a tape, the tire was 12'' wide, the inner bead was just under 10". This is over the 1 inch, but I had 8 inches of sidewall, and this was an offroad tire, on something that never saw 80 mph.
I don't know if there is a difference for slicks, and drag radials.