Judicious　partitioning　problems　on　graphs　ask　for　partitions　that　bound　several　quantities　simultaneously,　which　have　received　much　attention　lately.　Scott　(2005)　asked　the　following　natural　question:　What　is　the　maximum　constant　cd　such　that　every　directed　graph　D　with　m　arcs　and　minimum　outdegree　d　admits　a　bipartition　V(D)　=　V1　∪　V2　satisfying　min{e(V1,　V2),　e(V2,　V1)}　⩾　cdm?　Here,　for　i　=　1,　2,　e(Vi,　V3-i)　denotes　the　number　of　arcs　in　D　from　Vi　to　V3-i.　Lee　et　al.　(2016)　conjectured　that　every　directed　graph　D　with　m　arcs　and　minimum　outdegree　at　least　d　⩾　2　admits　a　bipartition　V(D)　=　V1　∪　V2　such　thatmin{e(V1,V2),e(V2,V1)}⩾(d−12(2d−1)+o(1))m.　In　this　paper,　we　show　that　this　conjecture　holds　under　the　additional　natural　condition　that　the　minimum　indegree　is　also　at　least　d.　©　2019,　Science　China　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.