The phrase “sleep tight” means to “sleep soundly” or “sleep well.” It probably comes from the words ``tight” and “tightly” which are often used to describe “soundly or securely”. The use of the phrase dates back to 1881 in Boscobel: The Novel by Emma M. During the time, variations of the classic rhyming bedtime salutation “Good night, sleep tight and don’t let the bedbugs bite” were commonly used.