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.