A coin wrapping machine includes an accumulator section and a coin wrapping section. The accumulator section assembles a coin stack and delivers the coin stack to the coin wrapping section. A puff of compressed air is blown against the coin stack to resist coin flutter while the coin stack is being delivered to the coin wrapping section. The coin wrapping section includes a drive roller and idler rollers that wrap a coin wrapper sheet around the coin stack. The idler rollers do not engage the leading tip portions of the wrapper sheets to reduce the likelihood of the wrapper sheets jamming against the idle rollers.