A story that is false: “When John came home at 3:30 a.m., he gave his mother some cock-and-bull story about having a flat tire on the way home.”
An improbable account, often an alibi; a mendacious farrago: He gives me this cock-and-bull story about six flat tires
[1620+; origin uncertain; the French term ''cock and donkey'' is analogous]