There was a 16" wheel option through 2006 for the X3. There was even a 15" option in 2004. Those wheels would likely work. Not sure if the calipers changed or not, but it would be worth asking your dealer. The same brake pads are listed for 2004 through 2007 (2008 is the same as 2007), so that is one indication that the 2006 16" wheels would work.

Good luck.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue