In　this　paper,　we　investigate　certain　deformations　B-q(g)　of　the　negative　part　U-q(-)(g)　of　quantized　enveloping　algebras　U-q(g).　An　algorithm　is　established　to　determine　when　a　given　B-q(g)　is　a　PBW-deformation　of　U-q(-)(g).　For　g　of　type　A(2)　and　B-2,　we　classify　PBW-deformations　of　U-q(-)(g).　Moreover,　we　explicitly　construct　some　PBW　bases　for　a　class　of　PBW-deformations　B-q(g)　of　U-q(-)(g).　As　an　application,　lorgov-Klimyk＇s　PBW　bases　for　the　no-standard　quantum　deformation　U＇(so(n,C))　of　the　unioversal　enveloping　algebra　U(so(n,C))　are　recovered.　(C)　2013　Elsevier　Inc.　All　rights　reserved.