Last year I picked up a used 883 for my wife with very low mileage. When we picked it up from the dealer, the salesman told my wife to remember to "clear it out" by revving the engine before starting off. I asked him what exactly he was talking about and he told me that all of the carbed sportys over a couple of years (I think he said 03-05) had a tendency to cough a little.
It was a hot day and needless to say, it did much more than just cough. If you twisted the throttle with any authority after idling down, you'd get a big belch and it would try to stall. I found this completely unacceptable, especially when my wife, who is a new rider, would be using the bike. She did a little riding right away, and sure enough, it was a real confidence breaker for her always worrying about the bike stalling on her.
I called the salesman back and he assured me that they all ran that way (it's normal??). I couldn't believe that the factory would allow a bike to be shipped running that way, so I started looking on the web to see if any others had the same trouble. Unbelievably, many others have the exact same symptoms! Apparently Harley had to make them run like shit to meet EPA standards.
I learned that other owners had luck by just increasing the idle jet a size or two. I tried that and saw some improvement, but hot weather still made her cough. I went up 3 sizes and had it at a minimum, but then it was too rich. I decided not to make any more carb changes until I modified the pipes and air cleaner. Why do it again right?
I put on V & H Short Shots, Stage I air cleaner, and re-worked the carb with a dynojet carb kit.
Now the bike runs 100% better! What a difference. Once in-a-while when it's hot you can get a pop after chopping back to idle quickly, nothing like before. It never seems like it's trying to stall now.
FYI The dynojet kit can be installed in stages, depending on the rest of your setup. The directions are very straight forward. I highly recommend the dynojet kit for anybody having similar problems.