The majority of lower blepharoplasties I've performed over the last 14 years have involved fat repositioning or redistribution.
Essentially, fat repositioning involves the release of fat from within the eyebag, pulling it downwards to fill in the tear troughs (if present). The fat is secured in position with dissolvable stitches. If there is more fat than required, some is removed. If there is insufficient fat, concurrent fat grafting would be beneficial.
As the fat is not disconnected from its blood supply, its survival is 100% ensuring a smooth finish; compared to fat grafting where survival is usually 50 to 70% in this region.
In my experience, fat repositioning gives a more durable result and avoids possible future hollowing which may be associated with other methods of eyebag removal which only remove fat. Fat repositioning is particularly useful in patients with tear troughs (the hollows beneath the eyebags).