A spiral conveyor and a method for taking up slack in a modular conveyor belt traveling a helical path. The spiral conveyor includes a rotating cylindrical drive drum with parallel drive members extending from the bottom to the top of the drum on its periphery. Each drive member includes an outwardly protruding ridge extending from the bottom to the top of the drum for engaging the inside edges of the belt. A motor-driven take-up shaft and shaft-mounted sprocket set takes up slack in the belt after its release from the drum. To control tension at the discharge of the belt from the drive drum, the take-up motor is normally operated in a closed-loop control mode, but switches to an open-loop constant-speed control mode when the take-up motor stalls.