  Call a simple graph $H$ of order $n$ well-separable, if by deleting a
separator set of size $o(n)$ the leftover will have components of size at most
$o(n)$. We prove, that bounded degree well-separable spanning subgraphs are
easy to embed: for every $\gamma >0$ and positive integer $\Delta$ there exists
an $n_0$ such that if $n>n_0$, $\Delta(H) \le \Delta$ for a well-separable
graph $H$ of order $n$ and $\delta(G) \ge (1-{1 \over 2(\chi(H)-1)} + \gamma)n$
for a simple graph $G$ of order $n$, then $H \subset G$. We extend our result
to graphs with small band-width, too.
