The transconjunctival blepharoplasty provides reduction in fat without undesired alteration in eye shape. It can, however, produce hollowness, and the skin is looser. It's a great operation for young patients with tight skin.The conventional lower blepharoplasty, including a blepharoplasty with a 'skin pinch' alters eye shape by pulling down on the lower eyelid. This leads to a rounding of the eye or pulling down on the corner. In skilled hands, this is effect is subtle but you can see it if you look closely at the before after pictures.For that reason we seldom do either. Rather, a sub ciliary sub orbicularis cheeklift allows the cheek to be elevated, avoiding downward traction on the lower eyelid. This is a very different concept for rejuvenation of the lower eyelid but it has served us well for the past 15 years and many hundreds of cases.
Generally most sophisticated eyelid surgeons anticipate these issues and propose a chemical peel with the lower blepharoplasty or alternative perform a skin pinch. Consider posting photographs so we have a better idea of your concerns. Filling the lower eyelid with a small amount of hyaluronic acid filler can soft or eliminate these issues and typically last about a year.