We shall discuss consistent examples of coideals (=complements of ideals in P(w)) distinguishing between covering properties of Menger, Scheepers, and variations thereof, thus answering some questions posed in an earlier work with Bella and Tokgoz. These examples could be obtained both by recursive constructions using certain equalities between cardinal characteristics, as well as by forcing. We also plan to mention potential applications in functional analysis as well to the problem of existence of non-meager P-filters.