Park and Pham's recent proof of the Kahn-Kalai conjecture was a major breakthrough in the field of graph and hypergraph thresholds. Their result gives an upper bound on the threshold at which a probabilistic construction has a $1-ε$ chance of achieving a given monotone property. While their bound in other parameters is optimal up to constant factors for any fixed $ε$, it does not have the optimal dependence on $ε$ as $ε\rightarrow 0$. In this short paper, we prove a version of the Park-Pham Theorem with optimal $ε$-dependence.