How to Help a Kitten Sleep. Part of the series: Puppy & Kitten Care. Most kittens that have just been fed tend to fall asleep easily, but you can help your kitten sleep by signaling that it's relaxation time and not playtime. Give your kitty and yourself a quiet evening with the aid of this free video on puppy and kitten care. Read more: http://www.ehow.com/video_8405850_kit...