In this paper we further study θ-Menger, θ-almost Menger and θ-weakly Menger properties [13] and investigate their relationships with other selective covering properties. We prove that in extremally disconnected semi-regular spaces, the properties viz. Menger, semi-Menger, α-Menger, θ-Menger, midly Menger are equivalent; and every finite power of a space X has the selection property S f in (θ-O, θ-O) if and only if X has the property S f in (θ-Ω, θ-Ω).