Yes. Keeping your newly permed hair safe at night can seem like a difficult task, but there are a few things that you can do. Using a regular cotton pillowcase can cause friction and undue damage to your permed hair. Try trading your cotton pillow in for a satin pillowcase; it will give your hair the freedom to move without causing damage. You can try tying your hair into a loose bun or even braids to help you sleep without incident.