  We study two objects concerning the Wiener sausage among Poissonian
obstacles. The first is the asymptotics for the \textit{replica overlap}, which
is the intersection of two independent Wiener sausages. We show that it is
asymptotically equal to their union. This result confirms that the localizing
effect of the media is so strong as to completely determine the motional range
of particles. The second is an estimate on the \textit{covering time}. It is
known that the Wiener sausage avoiding Poissonian obstacles up to time $t$ is
confined in some `clearing' ball near the origin and almost fills it. We prove
here that the time needed to fill the confinement ball has the same order as
its volume.
