Best Treatment for Red Veins on Eyelids and Undereyes?

Thank you for your question. Topical creams containing Vitamin K are an option for the small red veins, but challenging to fully treat. Veins in this area are more difficult to treat here due to their high risk.  I recommend seeing a Board Certified Dermatologist or Oculoplastic/Ophthalmologist to see you and treat these higher risk veins.  I hope this helps.

Under eye veins can vary in caliber and length, ranging from bluish varicose veins to light red spider veins. The treatment of larger varicose veins is very specialized and I have demonstrated my technique on the Doctors television show which can be found online. Treatment includes surgical removal with initiation of a skin brightening regimen to optimize skin thickness and collagen content. 
Associated dark pigmentation on the lower eyelid skin can be due to melasma, bluish veins, hemosiderin deposits, and hyperpigmentation.  
Topical regimens include: 
1.MelaClenz
2.Melarase AM
3.Melarase PM
4.Melapads
5.Replenish Retinoid Cream
Additional therapies for undereye rejuvenation include fractional laser, fractional RF, Covalent peels, and LED microneedling with Replenish serum. The video demonstrates an analysis of varicose veins.
Best, 
Dr. Karamanoukian
Realself100 Surgeon

These are fairly common problems in the lower eyelids and undereyes and in the upper eyelids and depending on their size (telangiectasiasa or varicose veins), can be treated with a number of different modalities, all of which should be in the armamentarium of the treating physician. In our laser office, we use sclerotherapy on the larger veins, ohmic thermolysis in some cases, RF treatment in others, lasers in most and microphlebectomy in the largest ones.