We show that in a super-reflexive Banach space, the conditionality constants $k_N\left(ℬ\right)$ of a quasi-greedy basis ℬ grow at most like $O\left({\left(logN\right)}^{1-\epsilon }\right)$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_p$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_N\left(ℬ\right)\approx logN$.