The most common and effective treatment for small veins is Sclerotherapy. It involves tiny injections of medication into the problem vessels. The medication causes the inside of these vessels to become "sticky" and then the walls stick together (sclerose) and the vessel closes off and disappears. This happens in the first 1-2 weeks after injection. Sclerotherapy can be used for vessels as tiny as 0.5mm. Although the most common area to have sclerotherapy is the legs, it can be performed for facial or torso vessels.
This form of treatment is safe and effective. It has been used for more that 100 years and is still considered the gold standard.