'99 Silverado exhaust/backfiring problem

I have a '99 Silverado with a Flowmaster 40 series muffler that is dumped. Usually, when I accelerate fast my truck sounds like it backfires when it shifts gears and almost seems like it is mis-firing at times. It also seems to fun kind of boggy as if it there is not enough compression in my exhaust system because my tail pipe ends right after the muffler. I was told that it could be backfiring because my exhaust is dumped right after the muffler and there is not enough back pressure, and that my problem could be solved by putting on a full tail pipe after the muffler. Does anyone know anything about this or have any suggestions as to what I should do? Could my truck be backfiring because my tail pipe is too short?

I have the identical problem with my 99 silverado (Stock 5.3L 120K miles).... I have checked around with other mechanics, replaced fuel filter and they all seem to think it could be a bad Cat Converter.. I am going to check it out this weekend and post the results...