A method for efficient wireless communications performed by a communications apparatus includes determining a cell according to a low priority list; and performing an attach procedure to try to attach to the cell for establishing an emergency call through the cell. The low priority list comprises information regarding a public land mobile network (PLMN) identity (ID), tracking area (TA) code, a cell ID and/or a closed subscriber group (CSG) ID of at least one attempted cell through which the communications apparatus has attempted but failed to establish an emergency call.