Covert　communications　can　hide　the　very　existence　of　wireless　transmissions　and　thus　are　able　to　address　privacy　issues　in　numerous　applications　of　the　emerging　Internet　of　Things　(IoT).　In　this　article,　we　adopt　channel　inversion　power　control　(CIPC)　to　achieve　covert　communications　in　Rayleigh　fading　wireless　networks,　where　a　transmitter　can　possibly　hide　itself　from　a　warden　while　transmitting　information　to　a　receiver.　The　CIPC　can　guarantee　a　constant　signal　power　at　the　receiver,　which　removes　the　requirement　that　the　receiver　has　to　know　the　channel　state　information　in　order　to　coherently　decode　the　transmitter＇s　signal.　Specifically,　we　examine　the　performance　of　the　achieved　covert　communications　in　terms　of　the　effective　covert　rate　(ECR),　which　quantifies　the　amount　of　information　that　the　transmitter　can　reliably　convey　to　the　receiver　subject　to　the　warden＇s　total　error　probability　being　no　less　than　some　specific　value.　The　noise　uncertainty　at　the　warden　serves　as　the　enabler　of　covert　communications.　For　fairness,　we　also　consider　noise　uncertainty　at　the　legitimate　receiver.　Our　examination　shows　that　increasing　the　noise　uncertainty　at　the　warden　and　the　receiver　simultaneously　may　not　continuously　improve　the　ECR　achieved　in　the　considered　system　model.