Pretty bad backfiring on downshifting.    Where do I start? 

You improved the breathing and changed the carb, and now you have a problem.  I would guess you need to re-jet your new carb.  If you have access to an air/fuel guage, adjust for 14.7:1 ant cruise, and 12.6:1 at full throttle.  Then fine tune from there.

Larry

Downshifting means slowing down, that's a no-no in a Corvette Hey Mike you have to send me some pictures with the side pipes, don't ya just love them!

Dave -- You slay me, brother!    The only thing I like less than slowing down, though, is the T-BONE at the crossroads! 

lets start at the beginning, if the the car ran fine before the header and muffler change and you did nothing else then my first question is  are the headers and mufflers new or used, if used the header flange might be warped and allowing air to be drawn into the primary pipe between the head, gasket, or flange, where warped, this will cause a backfire in the exhaust, did the car run fine for a while and then start to backfire, you have to re tighten the flange bolt 3-4 times after a run allowing the engine to be stone cold between tightenings to be sure they are tight,  you should also check where the muffler slips on to the collector at the front fender for leaks, also use the good thick flange  gaskets and locking header bolts, another reason for backfire in the exhaust is a  over rich condition in the carb, probley not the problem, cause by rights if anything it should be running a little leaner, in which case it would backfire through the carb. anips2009-05-22 15:08:32