Tire size and brand?

It sounds like you're running a 285/60/15 which would be ~11.2" wide and 28.5" tall.
If so, a 285/50/15 would keep almost exactly the same width but drop you down to ~26.2" diameter. Keep in mind that even though you're keeping the same width, you're still losing contact patch.
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@JeffisOld

What did I get wrong? The numbers came from a tire size calculator.