  In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the
polynomial algebra in three variables is wild. We fix a Z-grading on this
algebra and consider graded-wild automorphisms, i.e. such automorphisms that
can not be decomposed onto elementary automorphisms respecting the grading. We
describe all gradings allowing graded-wild automorphisms.
