If you are cleaning small or hard to reach areas of the doll, you can apply the solution with a cotton swab. The swab will enable you to reach those tricky areas that your cloth doesn't reach very well. When you are finished, double check the doll for any places you may have missed, and for any possible drips of cleaning solution you may have missed clearing away in the buffing process. Leave the hair pinned up, and place the doll in a warm dry place. It will take several hours to dry.
Humidity is death to a composition doll.
This makes the basement or garage, near the clothes dryer vent, a very poor choice for a drying area. If you have a roasting or baking rack, this makes an excellent tool for getting the doll dry quickly, by allowing air to circulate all around the doll. Work quickly, and in small stages. You want to be rubbing away the cleaning solution with the second, dry cloth, as quickly as possible. Apply the solution to small areas.