An arrangement in an anesthesia apparatus, the anesthesia apparatus comprising a filling device located by a vaporizer and an anesthetic bottle that fits the filling device, the filling device being provided with a valve device, which is arranged to open and close as needed. To provide a controlled discharging of anesthetic, the arrangement comprises a discharge space, which is connected to an interspace formed between the anesthetic bottle and the valve device located in the filling device when the anesthetic bottle is being pulled outward, and a closing member, which, as a result of the anesthetic bottle being pulled outward, is arranged to open a flow connection between the interspace and the discharge space before the connection between the anesthetic bottle and the filling device opens.