The present invention relates to a user equipment and a radio base station, and to related methods of enabling the radio base station to affect an energy saving in the system during a connection between the user equipment and the radio base station according to a priority level of the energy saving. The method comprises the step of detecting (210) a trigger received via a user interface of the user equipment, where the trigger is associated with the priority level of the energy saving in the system. It also comprises transmitting (220) an indicator of the priority level to the radio base station, allowing the radio base station to affect the energy saving in the system during the connection according to the priority level, by configuring different user or system related parameters.