A dispenser for sequentially dispensing web material from a plurality of rolls includes a carousel rotatably mounted in a dispenser body. The carousel includes a plurality of roll holders that extend parallel to an axis of rotation of the carousel. The carousel includes a sensor that senses whether a roll of web material on one of roll holders is depleted or substantially depleted. A movable trigger latch blocks rotation of the carousel until the roll of web material on the current roll holder is depleted or substantially depleted; at that point, the carousel rotates by gravity in a first direction.