A mother-and-daughter combination lock includes: a housing, a shackle lockable or unlockable in a first portion of the housing as controlled by a locking shaft and a plurality of dials and sleeves rotatably mounted in the housing; and a sliding door slidably held in the housing for covering and uncovering a security compartment recessed in a second portion of the housing as also controlled by the locking shaft, the dials and the sleeves, whereby either the shackle or the sliding door can be independently and individually locked or unlocked.