  In this paper, we investigate what selection principles properties are
possessed by small (with respect to the bounding and dominating numbers) unions
of spaces with certain (star) selection principles.. Furthermore, we give
several results about iterations of these properties and weaker properties than
paracompactness. In addition, we study the behaviour of these iterated
properties on $\Psi$-spaces. Finally, we show that, consistently, there is a
normal star-Menger space that is not strongly star-Menger.
