  We report numerical estimates of correlation lengths in 2D Potts models from
the asymptotic decay of the cluster-diameter distribution. Using this
observable we are able to verify theoretical predictions for the correlation
length in the disordered phase at the transition point for $q=10$, 15, and 20
with an accuracy of about $1%-2%$. This is a considerable improvement over
previous measurements using the standard (projected) two-point function.
