Monte Carlo calculations on lattices with large spatial volume show that the SU(3) deconfining phase transition is more weakly first order than previously thought. We have studied the transition for ${N}_{T}=4 \mathrm{and} 6$ on lattices of spatial volumes ${16}^{3}$, ${20}^{3}$, and ${24}^{3}$. The ${24}^{3}$\ifmmode\times\else\texttimes\fi{}4 calculations show a sharp first-order phase transition, yielding a latent heat $\frac{\ensuremath{\Delta}\mathcal{E}}{{T}^{4}}$ of 2.54\ifmmode\pm\else\textpm\fi{}0.12. The ${24}^{3}$\ifmmode\times\else\texttimes\fi{}6 calculations suffer greater finite-volume smearing, but suggest that $\frac{\ensuremath{\Delta}\mathcal{E}}{{T}^{4}}=2.48\ifmmode\pm\else\textpm\fi{}0.24$. Correlation lengths increase significantly near the transition, and the energy plus pressure of the ordered phase depends strongly on $\ensuremath{\beta}$.