A method performed in a wireless communication device for handling connection state changes in a wireless communication system, wherein the wireless communication device comprises at least two Subscriber Identity Modules, SIMs, in which a first SIM is in a first original connection state towards a first network node, a second SIM is in a second original connection state towards a second network node, the method comprising: determining whether a battery power in the wireless communication device is below a first threshold; when the battery power is below the first threshold, selecting a SIM out of the at least two SIMs for which to change its original connection state to a third connection state based on a connection characteristic parameter, wherein: the connection characteristic parameter is associated to at least one of: a) radio channel characteristics for the connection state associated to the respective SIMs, b) radio network capabilities for the connection state associated to the respective SIMs, c) Quality of Service, QoS, for the connection state associated to the respective SIMs, d) a cost for the connection state associated to the respective SIMs, and e) services provided by the connection state associated to the respective SIMs, the first and second original connection states are active mode, and the third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state, and is any one of an active mode with a different radio access technology, RAT, than the connection RAT of the selected SIM, an idle mode, or a detached state with occasional network attachments to poll received messages; and performing a connection state change for the selected SIM from its original connection state to the third connection state. determining whether a battery power in the wireless communication device is below a first threshold; when the battery power is below the first threshold, selecting a SIM out of the at least two SIMs for which to change its original connection state to a third connection state based on a connection characteristic parameter, wherein: the connection characteristic parameter is associated to at least one of: a) radio channel characteristics for the connection state associated to the respective SIMs, b) radio network capabilities for the connection state associated to the respective SIMs, c) Quality of Service, QoS, for the connection state associated to the respective SIMs, d) a cost for the connection state associated to the respective SIMs, and e) services provided by the connection state associated to the respective SIMs, the first and second original connection states are active mode, and the third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state, and is any one of an active mode with a different radio access technology, RAT, than the connection RAT of the selected SIM, an idle mode, or a detached state with occasional network attachments to poll received messages; and performing a connection state change for the selected SIM from its original connection state to the third connection state. the connection characteristic parameter is associated to at least one of: a) radio channel characteristics for the connection state associated to the respective SIMs, b) radio network capabilities for the connection state associated to the respective SIMs, c) Quality of Service, QoS, for the connection state associated to the respective SIMs, d) a cost for the connection state associated to the respective SIMs, and e) services provided by the connection state associated to the respective SIMs, the first and second original connection states are active mode, and the third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state, and is any one of an active mode with a different a) radio channel characteristics for the connection state associated to the respective SIMs, b) radio network capabilities for the connection state associated to the respective SIMs, c) Quality of Service, QoS, for the connection state associated to the respective SIMs, d) a cost for the connection state associated to the respective SIMs, and e) services provided by the connection state associated to the respective SIMs, the first and second original connection states are active mode, and the third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state, and is any one of an active mode with a different the first and second original connection states are active mode, and the third connection state is a connection state implying lower power consumption for the wireless communication device compared to its original connection state, and is any one of an active mode with a different radio access technology, RAT, than the connection RAT of the selected SIM, an idle mode, or a detached state with occasional network attachments to poll received messages; and performing a connection state change for the selected SIM from its original connection state to the third connection state.