The original tire on an Advance-Design 15" rim/wheel is a little larger diameter than the original tire on a 16" rim.

Also, you can find 15" and 16" light truck radial tires that are up to 3" larger diameter than the original bias-ply tires (31.5" compared to about 28.5") .

My 16" rims were 4.5" wide and the 15" rims were 5" wide. Radial tires for 5.5" rims were easily mounted on both sets of rims. I checked different vendors' on-line specifications for LT (light truck) radial tire rim-width before I went to a local supplier (Cooper) to buy and mount the tires (I used an inner tube and valve protector).