In　this　work,　we　adopt　channel　inversion　power　control　(CIPC)　to　achieve　covert　communications　aided　by　a　full-duplex　receiver.　Specifically,　the　transmitter　varies　the　power　and　phase　of　transmitted　signals　as　per　the　channel　to　the　receiver,　such　that　the　receiver　can　decode　these　signals　without　knowing　the　channel　state　information.　This　eliminates　the　required　feedback　from　the　transmitter　to　the　receiver,　which　aids　hiding　the　transmitter　from　a　warden.　The　truncated　CIPC　and　conventional　CIPC　schemes　are　proposed　and　examined,　where　for　truncated　CIPC　covert　transmission　ceases　when　the　channel　quality　from　the　transmitter　to　the　receiver　is　low,　while　for　conventional　CIPC　covert　transmission　always　occurs　regardless　of　this　channel　quality.　We　examine　their　performance　in　terms　of　the　achieved　effective　covert　throughput　(ECT),　which　quantifies　the　amount　of　information　that　the　transmitter　can　reliably　convey　to　the　receiver,　subject　to　the　constraint　that　the　warden＇s　detection　error　probability　is　no　less　than　some　specific　value.　Our　examination　shows　that　the　truncated　CIPC　scheme　can　outperform　the　conventional　CIPC　scheme　due　to　this　constraint.