The present invention concerns a device and method for reefing a portion of tubular film, the reefing device having at least one reefing finger and at least one drive unit. The drive unit has advancing means, which, for reefing the portion of tubular film, is brought into operative connection with the reefing finger at least at the height of a point of engagement, while enclosing the portion of tubular film, and moves the portion of tubular film in relation to the reefing finger. The device according to the invention and the method according to the invention are distinguished in particular in that the position of the at least one point of engagement can be changed along the reefing finger as reefing progresses or the position of the point of engagement on the reefing finger is changed.