From Longman Dictionary of Contemporary Englishsleep tightsleep tightspokenSLEEP said especially to children before they go to bed to say that you hope they sleep well Good night, Jenny. Sleep tight! → sleep
Examples from the Corpus
sleep tight• Good night, kids. Sleep tight!• With promises of endless ice cream when he awoke, Mama kissed her little son and bade him goodnight, sleep tight.• I don't sleep tight so that's all right. 