Laver [L] and others [G-S] have shown how to make the supercompactness
or strongness of kappa indestructible by a wide class of forcing noti
ons. We show, alternatively, how to make these properties fragile. Spe
cifically, we prove that it is relatively consistent that any forcing
which preserves kappa(<kappa) and kappa+, but not P(kappa), destroys t
he measurability of kappa, even if kappa, is initially supercompact, s
trong, or if I1(kappa) holds. Obtained as an application of some gener
al lifting theorems, this result is an ''inner model'' type of theorem
proved instead by forcing.