The invention relates to the filling of a frozen dessert product in a container, by performing the steps of : arranging at least one container to be filled on a slat conveyor, moving the container on the slat conveyor towards a dispensing nozzle, vertically displacing at least one slat supporting the container, and horizontally displacing the slat supporting the container in a direction perpendicular to the transport direction of the slat conveyor, while dispensing the product from the dispensing nozzle into the container.