This procedure is a lot more costly in the US but I had it done successfully in the Dominican Republic where I lived at the time and the results were satisfactory. Before starting the Dr. had me take an ultrasound to see what was causing my varicose veins and it appeared that I have "venous insufficiency". She stated that this is something that can be corrected with surgery but if I wanted a quick fix she could eliminate the superficial varicose veins through Sclerotherapy.
I had 10 sessions of injections (as not all veins can be done at once, specially when you have a lot like I do). All the veins that were injected disappeared instantly. I tend to bruise easily so at the end of each session I ended up with heavily bruised legs. You need to go home with your legs wrapped in tight elastic bandages and use these for a few days during the day.
The bruises completely disappear in about 2 weeks, when you need to go for the next session. I now still have varicose veins but mostly because I had another baby and varicose veins run in my family. I need to go back for a few more sessions but this may be something that people like me will need to continue doing each year, if we want decent legs.