A semiconductor structure is provided that has semiconductor fins having variable heights without any undue topography. The semiconductor structure includes a semiconductor substrate having a first semiconductor surface and a second semiconductor surface, wherein the first semiconductor surface is vertically offset and located above the second semiconductor surface. An oxide region is located directly on the first semiconductor surface and/or the second semiconductor surface. A first set of first semiconductor fins having a first height is located above the first semiconductor surface of the semiconductor substrate. A second set of second semiconductor fins having a second height is located above the second semiconductor surface, wherein the second height is different than the first height and wherein each first semiconductor fin and each second semiconductor fin have topmost surfaces which are coplanar with each other.