In　the　current　paper,　we　prove　the　11-total　choosability　of　planar　graphs　with　maximum　degree　Delta　＜=　8,　the　(Delta　+　1)-total　choosability　of　5-cycle-free　planar　graphs　with　maximum　degree　Delta　＞=　8,　the　5-total　choosability　of　graphs　with　maximum　degree　Delta　=　4　and　maximum　average　degree　mad　＜　3,　and　the　4-total　choosability　of　subcubic　graphs　with　maximum　average　degree　mad　＜　9/4.　(C)　2010　Elsevier　B.V.　All　rights　reserved.