Laser hair removal is not effective on light hair. It is great that your dark hair has been treated effectively, but now what to do for the light hairs?
Electrolysis is effective but can be time consuming, requiring mulitple sessions, and thus costly. Perhaps you can purchase a series of treatments at a discounted rate.
Other options include shaving - yes shaving, and it will NOT make the hair darker or thicker (I rountinely shave my fine ligth facial hair - think dermaplaning only a lot cheaper because done at home), plucking, waxing (these can cause irritation so be cautious), and use of depilatory creams or growth inhibiting cream - Vaniqa. Vaniqa is a prescription product that inhibits hair growth. Recommended use is twice a day, however, less applications may work for maintenance.