In this paper we conclude that the notion of a n-strongly (0-) minimal quasi-ideal and that of a regular, strongly (0-) minimal quasiideal coinside. Our related results, obtained independently from Clifford's results, present us with additional information on the last-named quasiideals. We give, as a by-product, a solution to a problem posed by L. Márki. Furthermore, we generalize two results of O. Steinfeld to the quasi-reflexive case, and on the other hand we sharpen the same results by means of n-strongly (0)-minimal quasi-ideals.