A method for selecting a core network slice, NS, for serving a wireless communication device, WCD, in a core network comprising at least one Management Function, MF, entity serving the WCD and at least one Repository Function, RF, entity (NRF1, NRF2) serving a plurality of core network slices NSs, (NSI#1, NSI#2), each comprising a plurality of Network Function, NF, entities the method being performed by a Slice Selection Function, SSF, entity operative in the core network, the method comprising: - obtaining ( 612, 616) NSI-running-status information indicating NSI-running-status for each NS to be monitored by: • sending a NSI-monitoring request towards each RF (NRF1, NRF2) that serves at least one NS (NSI#1, NSI#2) to be monitored, which request indicates the NSs to be monitored by the particular RF, and • receiving, from each RF (NRF1, NRF2) that received the NSI-monitoring request, a NSI-monitoring response originating from each RF serving at least one NS to be monitored, which NSI-monitoring response comprises NSI-information indicating NSI-running-status for each NS monitored by the particular RF, where the NSI-running-status comprises the number of NFs currently instantiated in the Network Slice Instance, NSI, and/or the work load status per NF in the NSI; and - receiving a NSI-selection request comprising NSI-selection information indicating at least one of NS (NSI#1, NSI#2) for serving the WCD; - selecting, based on the NSI-selection information and the NSI-running-status information, a selected NS (NSI#2) for serving the WCD. - obtaining ( 612, 616) NSI-running-status information indicating NSI-running-status for each NS to be monitored by: • sending a NSI-monitoring request towards each RF (NRF1, NRF2) that serves at least one NS (NSI#1, NSI#2) to be monitored, which request indicates the NSs to be monitored by the particular RF, and • receiving, from each RF (NRF1, NRF2) that received the NSI-monitoring request, a NSI-monitoring response originating from each RF serving at least one NS to be monitored, which NSI-monitoring response comprises NSI-information indicating NSI-running-status for each NS monitored by the particular RF, where the NSI-running-status comprises the number of NFs currently instantiated in the Network Slice Instance, NSI, and/or the work load status per NF in the NSI; and • sending a NSI-monitoring request towards each RF (NRF1, NRF2) that serves at least one NS (NSI#1, NSI#2) to be monitored, which request indicates the NSs to be monitored by the particular RF, and • receiving, from each RF (NRF1, NRF2) that received the NSI-monitoring request, a NSI-monitoring response originating from each RF serving at least one NS to be monitored, which NSI-monitoring response comprises NSI-information indicating NSI-running-status for each NS monitored by the particular RF, where the NSI-running-status comprises the number of NFs currently instantiated in the Network Slice Instance, NSI, and/or the work load status per NF in the NSI; and - receiving a NSI-selection request comprising NSI-selection information indicating at least one of NS (NSI#1, NSI#2) for serving the WCD; - selecting, based on the NSI-selection information and the NSI-running-status information, a selected NS (NSI#2) for serving the WCD.