A method for filling containers using a filling liquid stored in a tank and delivered using at least one filling head including a spout endpiece provided with a bearing seat for a neck of a container, the spout endpiece being crossed by a filling tube connected to the tank and delimiting with the spout endpiece, at least part of an air return circuit, the filling tube delimiting an exit passage for the liquid which is opened or closed by means of an obturation device, the method including the following steps for the filling of a container: - making the neck of the container bear on the seat by engaging the spout endpiece of the spout inside the container; - translating the filling tube inside the container from a high position to a low position in the vicinity of the bottom of the container; - putting in communication with the interior of the container, the air return circuit put at atmospheric pressure so that it empties of its liquid; - when the filling tube occupies its low position, opening the exit passage of the filling tube in order to ensure the exit of the liquid and put the air return circuit in communication with a pressurized chamber to ensure a slow flow of the liquid; - when the exit passage of the filling tube is immersed in the liquid, putting the air return circuit at atmospheric pressure to increase the flow of the liquid; - moving the filling tube while keeping the liquid exit passage immersed, towards a leveling position for which the filling tube is engaged inside the container at a depth corresponding to the level of the liquid inside the container; - during the filling end phase, putting the air return circuit in communication with the pressurized chamber to slow down the flow of the liquid and move the filling tube to its leveling position; - waiting for the stabilization of the liquid level with a return of liquid in the air return circuit before closing the air return circuit; - and closing the exit passage of the filling tube to stop the exit of the liquid. - making the neck of the container bear on the seat by engaging the spout endpiece of the spout inside the container; - translating the filling tube inside the container from a high position to a low position in the vicinity of the bottom of the container; - putting in communication with the interior of the container, the air return circuit put at atmospheric pressure so that it empties of its liquid; - when the filling tube occupies its low position, opening the exit passage of the filling tube in order to ensure the exit of the liquid and put the air return circuit in communication with a pressurized chamber to ensure a slow flow of the liquid; - when the exit passage of the filling tube is immersed in the liquid, putting the air return circuit at atmospheric pressure to increase the flow of the liquid; - moving the filling tube while keeping the liquid exit passage immersed, towards a leveling position for which the filling tube is engaged inside the container at a depth corresponding to the level of the liquid inside the container; - during the filling end phase, putting the air return circuit in communication with the pressurized chamber to slow down the flow of the liquid and move the filling tube to its leveling position; - waiting for the stabilization of the liquid level with a return of liquid in the air return circuit before closing the air return circuit; - and closing the exit passage of the filling tube to stop the exit of the