We report a fairly detailed finite-size scaling analysis of the first-
order phase transition in the three-dimensional 3-state Potts model on
cubic lattices with emphasis on recently introduced quantities whose
infinite-volume extrapolations are governed only by exponentially smal
l terms. In these quantities no asymptotic power series in the inverse
volume are involved which complicate the finite-size scaling behaviou
r of standard observables related to the specific-heat maxima or Binde
r-parameter minima. Introduced initially for strong first-order phase
transitions in q-state Potts models with ''large enough'' q, the new t
echniques prove to be surprisingly accurate for a q value as small as
3. On the basis of the high-precision Monte Carlo data of Alves et al.
[Phys. Rev. B 43 (1991) 5846], this leads to a refined estimate of be
ta(t) = 0.550565(10) for the infinite-volume transition point. (C) 199
7 Elsevier Science B.V.