This solution may not be as silly as it sounds on first blush.
The bulge of fat is due to a bulge in the infraorbital fat behind the orbital septum. Transconjunctival blepharoplasty removes the fat, causing it to bulge less.
The hollowness most patients complain of is lower than the infraorbital fat bulge. There are two basic solutions to this problem:
1. Take the existing fat and redistribute it. This requires dividing the orbital septum at the arcus marginalis, a maneuver that can predispose to pulling down of the lower eyelid. This can be done through an incision in the lower eyelid and also through a transconjunctival incision.
2. Take the fat out of the transconjunctival sac and then put in separately a graft into the hollow area below the eye
Of the two, I have come full circle and no longer do fat repositioning. The grafts tend to clump and retract to where they had been previously. Often, the lower eyelid bulge returns. I think this is due to the fat still being attached to the lower eyelid fat pocket. If the fat is detached in order to avoid this problem, it becomes no different than a separately placed graft. Plus the arcus marginalis layer has been violated, predisposing in my opinion to the potential of scar formation. The most quoted series in the literature is only 24 patients, far too low to be confident of the safety of dividing the arcus marginalis method, in my opinion. I have seen plenty of unhappy repositioning patients where they did get alteration in eye shape (usually drooping, usually subtle but nonetheless there).
So we are back to square one, as they say.
I prefer to reduce transconjunctival fat and then place separate grafts, but not fat injection, where the grafts are largely traumatized, but untraumatized fat fascial grafts (LiveFill (R), almost always in combination with an ultrashort incision cheeklift (USIC). This elevates cheek volume.
Even with these 3 measures, patients must expect conservative results. That's how tricky the under eye area is if you don't want to subject the patient to great risk of lower eyelid eye shape change.
Just my opinion.