The "At witt's End Backfire Cure"

 I report this as a last ditch effort for those who may experience extreme situations where 
their bikes are persistently backfiring through the intake OR exhaust, AND conventional 
efforts to fix the problem prove fruitless. 

It is not a panacea for problems that might be fixed through normal jetting and adjustments.
I do want to stress that this is not the best way to fix MOST backfiring problems. 
Usually the correct fix is performed with alterations to jetting and insurance that the intake and exhaust systems are sealed.

My own Road Star has been plagued with vicious intake backfiring since it was new. 
The backfiring has frequently been so forceful that stalling the engine was
common and at least twice it reversed the engine's rotation.

The Yamaha
   factory rep couldn't do a thing with it, while it was under warranty and it has
   largely resisted my efforts as well. I had managed to reduce the intake
   backfiring a lot by reducing the accelerator pump volume and adjusting the pilot
   fuel system. That also reduced the stalling by 90% and eliminated the potential
   for engine reversal. 

But the backfiring refused to be fully exorcised. Recently I
   filled the pilot air correction with solder and then drilled it to .031" (from an
   original approximate size of .040"). 

Because the jets are brass, I find it easier to clean them up good and solder
   them closed. Then drilling the solder to the desired hole diameter is easy with a
   #1~#80 drill index and a Dremel tool. Some people might be tempted to epoxy
   the jet closed and then drill, but epoxy is less secure, harder to fill such a small
   hole and may chip out when the drill is put to it.

It has not popped up the intake even once in the last 200 miles. Again, end of problem.

While they do make alternate air correction jets (as I recall ours is a #100), I've
   never known a shop that stocks them and, in fact, few would know who to
   order them from. Sudco (http://www.sudco.com/) would probably be the best
   source, but I don't think they do retail.