Methods, wireless device (120; 400) and wireless communication network (100), such as a network node (110; 600) thereof, for managing downlink signal information. The downlink signal information being information about signal quality and/or signal strength received by the wireless device (120) in a downlink. The wireless device (120) sends (203; 302), to the wireless communication network (100), a message indicating said obtained downlink signal information and which message is associated with the wireless device (120) requesting access to the wireless communication network (100). The downlink information being indicated in the message by a range that indicates how much the obtained downlink signal information exceeds a certain threshold. The range is determined based on a certain factor that the wireless communication network (100) has informed the wireless device (120) about.