  In this paper we construct open Stein neighbourhoods of compact sets of the
form $A\cup K$ in a complex space, where $K$ is a compact holomorphically
convex set, $A$ is a compact complex curve with boundary $bA$ of class
$\mathscr C^2$ which may intersect $K$, and $A\cap K$ is $\mathscr
O(A)$-convex.
