Deep Pocket Sheets With the increasing popularity of thicker mattresses, pillowtop mattresses and featherbeds; we've made sure to keep up with this trend by offering the highest quality sheets with deeper pockets. Our Lyric sheets by Peacock Alley fit mattresses up to 17 inches deep. Many of our styles, including 1000 Egyptian, 1000 Egyptian Stripe, 500 Sateen Couture and 600 Egyptian fit mattresses up to 18 inches deep. Four of our Peacock Alley sheeting styles are cut extra deep to accommodate any mattress up to 21 inches deep!