Let be the class of all left -modules which has a projective resolution by finitely generated projectives. An exact sequence of right -modules is called neat if the sequence is exact for any . An exact sequence of left -modules is called clean if the sequence 0 →HomR(G,M) →HomR(G,N) →HomR(G,L) → 0 is exact for any . We prove that every -module has a clean-projective precover and a neat-injective envelope. A morphism of right -modules is called a neat-phantom morphism if for any . A morphism of left -modules is said to be a clean-cophantom morphism if for any . We establish the relationship between neat-phantom (respectively, clean-cophantom) morphisms and neat (respectively, clean) exact sequences. Also, we prove that every -module has a neat-phantom cover with kernel neat-injective and a clean-cophantom preenvelope with cokernel clean-projective.