  Whereas set-valued tableaux are the combinatorial objects associated to
stable Grothendieck polynomials, hook-valued tableaux are associated to stable
canonical Grothendieck polynomials. In this paper, we define a novel uncrowding
algorithm for hook-valued tableaux. The algorithm ``uncrowds'' the entries in
the arm of the hooks and yields a set-valued tableau and a column-flagged
increasing tableau. We prove that our uncrowding algorithm intertwines with
crystal operators. An alternative uncrowding algorithm that ``uncrowds'' the
entries in the leg instead of the arm of the hooks is also given. As an
application of uncrowding, we obtain various expansions of the canonical
Grothendieck polynomials.
