  We prove a revised version of Laver's indestructibility theorem which
slightly improves over the classical result. An application yields the
consistency of $(\kappa^+,\kappa)\notcc(\aleph\_1,\aleph\_0)$ when $\kappa$ is
supercompact. The actual proofs show that $\omega\_1$-regressive Kurepa-trees
are consistent above a supercompact cardinal even though ${\rm MM}$ destroys
them on all regular cardinals. This rather paradoxical fact contradicts the
common intuition.
