  We discuss the zero-temperature susceptibility of elastic manifolds with
quenched randomness. It diverges with system size due to low-lying local
minima. The distribution of energy gaps is deduced to be constant in the limit
of vanishing gaps by comparing numerics with a probabilistic argument. The
typical manifold response arises from a level-crossing phenomenon and implies
that wetting in random systems begins with a discrete transition. The
associated ``jump field'' scales as $<h > \sim L^{-5/3}$ and $L^{-2.2}$ for
(1+1) and (2+1) dimensional manifolds with random bond disorder.
