The easiest way to serve a peep into the string is to just use a series of overhand knots. Start a couple of inches away from the peep, where the split in the string is easy to push together. Tie one knot on top of the string, the next one underneath, next one on top, then underneath again. Pull each knot tight before doing the next one. Keep alternating like that until you get the serving about 1/2" long, then finish off with a sqare knot and melt the ends of the serving thread.

One serving above and one below the peep. Then slide the two servings toward the peep to clamp it in place. It's best to wax the string before tying so the servings will slide easier.