I bought a 2005 S40 on September 12. Very nice motorcycle with low mileage and no corrosion. Made purchase with no test ride (cautious seller). Have put on 150 miles since purchase and very happy. But noticed the backfiring. Started research, including this site. Today, I removed the brass plug and adjusted low end mixture. Also, removed the spacer on the slide needle. All went well.
I removed the brass plug by drilling it out with a drill bit slightly smaller than the casing around the plug. I was careful not to let the drill bit touch the head of the adjustment screw. It really was a 'piece of cake." By the way, there was a small hole in the middle of the brass plug. I stuck a needle through the hole and determined that there was about a 1/4 inch space between the outer face of the plug and the face of the adjustment screw.
As suggested, I turned out the low end mixture screw until idle speed peaked. A half turn counterclockwise. During test drive, noticed an increase in power and smoothness in acceleration. Backfire is less but still offers a minor "pop" now and then just to let me know it's still happy.
Other than having to remove the seat and the tank, this was an easy fix. No need to remove the carb. Just be careful working in and around the diaphragm, especially during replacement of the spring and cover.
Two day later - In my previous post, I recounted my "success" with removing the spacer on the jet needle and adjustment of the idle mixture screw. In the past two days, my "success" has proven less so. My engine started running lean, not rich! Yes! That's correct! Leaner! More pronounced backfires and weak acceleration, especially from idle. I progressively richened the idle mixture with no improvement. So, today, I replaced the spacer (Smart not to have thrown it away!) and now it runs just fine. And the idle mixture adjustment seems to make a substantial difference. Consequently, I don't recommend removing the spacer. Leave it alone. BTW, the brass plug in my carb was 9/64 thick.