The crossing number cr(G) of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number pcr(G) is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number ocr(G) is the minimum number of pairs of edges that cross an odd number of times. Clearly, ocr(G) ≤ pcr(G) ≤ cr(G). We construct graphs with 0.855 · pcr(...