  We prove that, for arbitrary three-dimensional transformation-based
invisibility cloaking of an object above a ground plane or of isolated object,
there are practical constraints that increase with the object size. In
particular, we show that the cloak thickness must scale proportional to the
thickness of the object being cloaked, assuming bounded refractive indices, and
that absorption discrepancies and other imperfections must scale inversely with
the object thickness. For isolated objects, we also show that bounded
refractive indices imply a lower bound on the effective cross-section.
