A cord enclosure assembly to encase one or more lift cords extending from the headrail of an architectural covering, such as a blind or shade system, is disclosed, for the purpose of avoiding exposed cords capable of creating a hazardous loop. The cord disclosure assembly comprises an enclosure having a pivot cup portion and an adaptor. The adaptor is configured to be selectively attached to the pivot cup portion about a pivot point. The adaptor is also configured to connect the enclosure to the headrail about a swivel point. At least one of the pivot point and the swivel point at a top of the enclosure allows the enclosure to swivel, or move in a lateral direction when attached to the headrail. This lateral movement allows the enclosure to be positioned substantially horizontally such that it may be stored under the headrail behind the blind or shade assembly.