Let $K(r)$ be the 3-manifold obtained by 
a Dehn surgery on a hyperbolic knot $K$ in the 3-sphere 
along a slope $r \ne \infty$. 
We show that 
if $|r| > 3 \cdot 2^{7/4} g$, then 
$K(r)$ is an irreducible 3-manifold with 
infinite and word-hyperbolic fundamental group, 
where $g$ denotes the genus of $K$.