  A minimal surface of general type with $p_g(S)=0$ satisfies $1\le K^2\le 9$
and it is known that the image of the bicanonical map $\fie$ is a surface for
$K_S^2\geq 2$, whilst for $K^2_S\geq 5$, the bicanonical map is always a
morphism. In this paper it is shown that $\fie$ is birational if $K_S^2=9$ and
that the degree of $\fie$ is at most 2 if $K_S^2=7$ or $K_S^2=8$.
  By presenting two examples of surfaces $S$ with $K_S^2=7$ and 8 and
bicanonical map of degree 2, it is also shown that this result is sharp. The
example with $K_S^2=8$ is, to our knowledge, a new example of a surface of
general type with $p_g=0$.
