Given a bipartite graph , a 2-layered drawing consists of placing nodes in the first node set V on a straight line and placing nodes in the second node set W on a parallel line . For a given ordering of nodes in W on , the one-sided crossing minimization problem asks to find an ordering of nodes in V on so that the number of arc crossings is minimized. A well-known lower bound LB on the minimum number of crossings is obtained by summing up over all node pairs , where denotes the number of crossings generated by arcs incident to u and when u precedes in an ordering. In this paper, we prove that there always exists a solution whose crossing number is at most if the minimum degree of a node in V is at least 5.