I am a big fan of the Kiehl's product with Vitamin C: I use everyday the
Powerful Strength line reducing concentrate and it really has a visible and incredible effect on overall brightness, quality of the skin, smoothness and fine lines.
I've tried
the eye version for two weeks thanks to one of their so-called luxe samples (quite big, actually a miniature version more than a sample) and the effect is even more amazing, you put it on and immediately you're just like "WOW!": no puffyness, no dark circles, no lines, you see only extreme brightness and freshness.
I don't know if it improves the situation of your under-eye skin in the very long term but it contains pure vitC at more than 10% concentration so it should (the serum I told you above does, and they're almost the same formula)
If I were you, I would surely try them out, also because the quality/price ratio is excellent (much better than other Lancome, Chanel and Dior products of the same type that I've tried)
I saw you are from Genève Adrina, and I see that Kiehl's should have a corner in Globus ;-)