Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

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.