After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ. In a delightful argument, Laver [L78] proved that any supercompact cardinal κ can be made indestructible by <κ-directed closed forcing. This indestructibility, however, is evidently not itself indestructible, for it is always ruined by small forcing: in [H96] the first author recen...