  The Erd\H{o}s-Simonovits stability theorem states that for all \epsilon >0
there exists \alpha >0 such that if G is a K_{r+1}-free graph on n vertices
with e(G) > ex(n,K_{r+1}) - \alpha n^2, then one can remove \epsilon n^2 edges
from G to obtain an r-partite graph. F\"uredi gave a short proof that one can
choose \alpha=\epsilon. We give a bound for the relationship of \alpha and
\varepsilon which is asymptotically sharp as \epsilon \to 0.
