Over in UK we are told to make to fit a piece of wood which will be 41/2inch deep or 4inch .i would cut along the length and add another piece2inch without seam allowances. The sew seams it could make a pleat check it doesn't show over the top. Does your sleeve fit from edge to edge it should do I order to hang correctly.
I have said add extra because with the word rod it sounded round shape. In UK the shape is rectangle and you definately need plenty of room.
Good luck in the shows.