This article is a continuation of study of star-Menger selection properties in line of (Kočinac, 2009, 2015), where we mainly use covers consisting of G δ sets with certain additional condition. It is observed that star-Mengerness is equivalent to the fact that every such type of cover of a space has a countable subcover. We improve this result by considering 'subcovers of cardinality less than b' instead of 'countable subcovers', which is our primary observation. We also show that it is possible to produce non normal spaces using box products and dense star-Menger subspaces.