  Let $\Gamma$ be a discrete group of isometries acting on the complex
hyperbolic $n$-space $\mathbb{H}^n_\mathbb{C}$. In this note, we prove that if
$\Gamma$ is convex-cocompact, torsion-free, and the critical exponent
$\delta(\Gamma)$ is strictly lesser than $2$, then the complex manifold
$\mathbb{H}^n_\mathbb{C}/\Gamma$ is Stein. We also discuss several related
conjectures.
