LetRbe a ring with identity and letbe a finite direct sum of relatively protectiveR-modulesMiThen it is proved thatMis lifting if and only ifMis amply supplemented andMiis lifting for all 1 ≤i≤n.Letbe a finite direct sum ofR-modulesMi. We prove thatMis (quasi-) discrete if and only ifare relatively projective (quasi-) discrete modules. We also prove that, for an amply supplementedR-moduleM=M1⊕M2such thatM1andM2have the finite exchange propertyMis lifting if and only ifM1andM2are lifting and relatively small projectiveR-modules and every co-closed submoduleNofMwithM=N+M1=N+M2is a direct summand ofM.Finally, we prove that, for a ringRsuch that every direct sum of a liftingR-module and a simpleR-module is lifting, every simpleR-module is smallM-projective for any liftingR-moduleM.