A tissue dispenser comprising: (a) a housing and cover that attach together and form an interior region for holding multiple tissue rolls and a dispenser opening for dispensing tissue from the dispenser interior, the housing having a back wall for mounting on a vertical wall; (b) a first roll holder located within the interior region, the first roll holder comprising a first back panel and a first mandrel extending from the first back panel, the first back panel is constructed to rotate, relative to the housing, between a locked position and an unlocked position, and the first mandrel is constructed to receive a first tissue roll; (c) a second roll holder located within the interior region, the second roll holder comprising a second back panel and second mandrel extending from the second back panel, the second back panel is constructed to rotate relative to the housing, between a locked position and an unlocked position, and the second mandrel is constructed to receive a second tissue roll; and (d) a door constructed to move within the dispenser opening between a first position and a second position so that when the door is provided in the first position, tissue can be dispensed from the first tissue roll provided on the first mandrel, and when the door is provided in the second position, tissue can be dispensed from the second tissue roll positioned on the second mandrel, wherein the door is constructed so that when the door is provided in either the first position or the second position and tissue is dispensing from either the first roll or the second roll, then the door is unable to move to the other of the first position or the second position until the tissue being dispensed is exhausted, wherein the first roll holder and second roll holder are rotatably connected to the housing, and wherein the first mandrel and the second mandrel are perpendicular to the back wall of the housing in the locked position. (a) a housing and cover that attach together and form an interior region for holding multiple tissue rolls and a dispenser opening for dispensing tissue from the dispenser interior, the housing having a back wall for mounting on a vertical wall; (b) a first roll holder located within the interior region, the first roll holder comprising a first back panel and a first mandrel extending from the first back panel, the first back panel is constructed to rotate, relative to the housing, between a locked position and an unlocked position, and the first mandrel is constructed to receive a first tissue roll; (c) a second roll holder located within the interior region, the second roll holder comprising a second back panel and second mandrel extending from the second back panel, the second back panel is constructed to rotate relative to the housing, between a locked position and an unlocked position, and the second mandrel is constructed to receive a second tissue roll; and (d) a door constructed to move within the dispenser opening between a first position and a second position so that when the door is provided in the first position, tissue can be dispensed from the first tissue roll provided on the first mandrel, and when the door is provided in the second position, tissue can be dispensed from the second tissue roll positioned on the second mandrel, wherein the door is constructed so that when the door is provided in either the first position or the second position and tissue is dispensing from either the first roll or the second roll, then the door is unable to move to the other of the first position or the second position until the tissue being dispensed is exhausted,