I don't think you can actively try to trade down. Showing that you are too anxious isn't a good strategy. Teams that are willing to trade down are merely going to announce their willingness and wait to see if there are any offers. Unless they hear an offer that significantly improves the overall value of their picks, they'll stand pat.
Again, it isn't that trading down is a bad idea....but who is saying, "we need to trade up to the 4 spot"? It takes 2 to tango.