An improved pre-factor for the random coding bound is proved. Specifically, for positive dispersion channels, if a certain regularity condition is satisfied, then for any ∊ > 0 a pre-factor of 0(N−½(1−∊+ρ∗w(R))) is achievable for rates above the critical rate, where ρ∗w (R) is related to the slope of the random coding bound at rate R. If the regularity condition is not satisfied, then a pre-factor of 0(N−½) is achievable. Recent work of the authors shows that the former case is nearly the best possible.