I guess 15" tires are not that popular anymore, and don't think many new cars even have that size wheel.
These days, 15" tires are usually the 'base' option on cars with much lower load ratings, I.E., subcompacts and compacts.
Back when my Caprice had 15" wheels I first switched over to a 16" wheel before getting the Impala 17's. The most important factor to me was getting a 16" tire that had the same overall diameter as the stock tire.
If you just want four pieces of bubblegum for tires, stick to whatever tire size you think is 'required'.
If one wants a better selection of somewhat better tires, just make sure you don't go under the minimum load rating for your car (98 for the B-car, 100 for the D-car), which will naturally lead to shopping either
If one wants a significantly better selection of significantly better tires, upgrade to a 17" or 18" wheel.
I suppose 16" wheels also allow for a better selection of tire options, I just have no experience with 16" tire choices (but quickly perusing TireRack's availability makes me lean toward 235/70R16, or 275/60R16).
Whichever tire size provides the best tire for my needs / wants and exceeds the minimum load rating (98 for the B-car) gets my money.
FWIW I ran a 235/60/16 and these were a hard find unless I wanted to shell out good money for the Michelin's which were a heck of a tire and had them at first … MVX4?? I later settled on a 225/60/16 that was offered by a lot of other vendors and much more cost effective albeit a little shorter tire.
Have you considered 235/70R16 or 275/60R16 yet?
For those of you who are afraid of your speedometers being 'off', this is the ImpalaSS Forum, by now, it should be easy to find someone local who will reprogram your speedo for about $50 or so.
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