Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,{\cal O}), \ldots , H^{n-1}(X,{\cal O})$ are of finite dimension (as complex vector spaces). We show that $X$ is Stein (resp., $1$-convex) if, and only if, $X$ is holomorphically spreadable (resp., $X$ is holomorphically spreadable at infinity). \endgraf This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for $1$-convexity.