  We study the parameterized complexity of separating a small set of vertices
from a graph by a small vertex-separator. That is, given a graph $G$ and
integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and
$|N(X)| \le t$. We show that
  - the problem is fixed-parameter tractable (FPT) when parameterized by $t$
but W[1]-hard when parameterized by $k$, and
  - a terminal variant of the problem, where $X$ must contain a given vertex
$s$, is W[1]-hard when parameterized either by $k$ or by $t$ alone, but is FPT
when parameterized by $k + t$.
  We also show that if we consider edge cuts instead of vertex cuts, the
terminal variant is NP-hard.
