High　coding　complexity　is　an　obstruction　when　promoting　the　HEVC　standard.　In　this　paper,　we　propose　a　complexity　control　scheme　for　HEVC,　which　improves　our　previous　work　by　employing　a　finer-grained　complexity　allocation　scheme　and　mode　sorting.　In　CTU-level　complexity　allocation,　the　time　budget　is　allocated　to　each　CTU　proportionally　to　its　estimated　complexity.　Then,　the　time　budget　for　a　CTU　is　further　allocated　to　each　CTU　quadtree　depth　according　to　its　probability　of　being　the　dominant　depth.　At　last,　a　subset　of　modes　are　selected　to　reach　the　target　complexity　based　on　mode　sorting.　Compared　with　our　previous　work　of　which　the　least　supported　complexity　ratio　is　40%,　the　proposed　scheme　further　reduces　the　lower　bound　of　the　ratio　range　to　20%.　©　2018　IEEE.