A conveyor device having a rotor and container carriers that suspend containers around the rotor includes a container support to support the sides of the suspended containers. The container support has an outer container guide with a height-adjustable outer container support surface that defines a tapered surface surrounding a machine axis about which the rotor rotates. The outer container support surface supports the containers on a radially outward portion of their surface and an inner container support surface supports the containers on a radially inward position of their lateral surface. The two support surfaces define a receptacle that receives the container's base. The receptacles width decreases as a function of distance from the container carriers. The inner container support surface is height-adjustable for adapting the container support device to different container base diameters.