I fish tungsten on all my small beadhead flies. You can fish two #18 zebra midges and get by without adding split shot for most situations on the Caney. It will sink better than lead. On the flies without dealing with low water they seem to be carried further sinking. The tung heads will get down in a shorter distance. I know I am talking really small in shallower water than you are but I believe the principal would transfer over. That is why the sinking fly lines on the market are coated in tungsten powder to give its sinking quality...does take much.
Here is the size #18-#20 of those midges.
