  A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient
dominating set} (\emph{e.d.s.}\ for short) of $G$ if every vertex of $G$ is
dominated by exactly one vertex of $D$. The \emph{Efficient Domination} (ED)
problem, which asks for the existence of an e.d.s.\ in $G$, is known to be
\NP-complete for $P_7$-free graphs, and even for very restricted $H$-free
bipartite graph classes such as for $K_{1,4}$-free bipartite graphs as well as
for $C_4$-free bipartite graphs while it is solvable in polynomial time for
$P_7$-free bipartite graphs as well as for $S_{2,2,4}$-free bipartite graphs.
Here we show that ED can be solved in polynomial time for $P_8$-free bipartite
graphs.
