Dispenser (10) for dispensing rolls of sheet material including a housing (12) configured to rotationally support a primary roll of sheet material and a backup roll of sheet material inside the housing. The housing also includes an exit port (24). The dispenser further includes a dispensing control member (60) moveably positioned substantially within and partially blocking the exit port. The dispensing control member is configured to substantially restrict rotation of the backup roll of sheet material prior to substantial depletion of the primary roll of sheet material.