A module is called semi-perfect iff every factor module has a projective cover. A module is defined to be supplemented iff every submodule has a supplement. F. Kasch and E. A. Mares have shown that M is a semi-perfect module iff M is supplemented [Nagoya Math. J. 27, 525-529 (1966; Zbl 0158.289)]. The author shows that M is semi-perfect if and only if M is supplemented by supplements which have projective covers. The semi-perfectness of M is also equivalent to the statement that M is amply supplemented by supplements with projective covers. Here a module M is defined to the amply supplemented iff \(M=A+B\) implies that A has a supplement in B. The results are also extended to F-semi-perfect, finitely generated modules M. These are finitely generated modules M such that every factor module by a finitely generated submodule has a projective cover [cf. W. Jansen, Commun. Algebra 6, 617-637 (1978; Zbl 0374.16019)].