We prove the minimal pseudo-Anosov translation length in the curve complex behaves like (1/ϗ(S_g,n)²) for sequences where g=rn for some r∈Q. We also show that if the genus is fixed as n→ ∞ then the behavior is (1/|ϗ(S_g,n)|). This extends results of Gadre and Tsai and answers a conjecture of theirs in the affirmative.