  We consider the large-time behavior of the solution $u\colon
[0,\infty)\times\Z\to[0,\infty)$ to the parabolic Anderson problem $\partial_t
u=\kappa\Delta u+\xi u$ with initial data $u(0,\cdot)=1$ and non-positive
finite i.i.d. potentials $(\xi(z))_{z\in\Z}$. Unlike in dimensions $d\ge2$, the
almost-sure decay rate of $u(t,0)$ as $t\to\infty$ is not determined solely by
the upper tails of $\xi(0)$; too heavy lower tails of $\xi(0)$ accelerate the
decay. The interpretation is that sites $x$ with large negative $\xi(x)$ hamper
the mass flow and hence screen off the influence of more favorable regions of
the potential. The phenomenon is unique to $d=1$. The result answers an open
question from our previous study \cite{BK00} of this model in general
dimension.
