Power back-off performances of a new variant power-combining Class-E amplifier under different amplitude-modulation schemes such as continuous wave (CW), envelope elimination and restoration (EER), envelope tracking (ET) and outphasing are for the first time investigated in this study. Finite DC-feed inductances rather than massive RF chokes as used in the classic single-ended Class-E power amplifier (PA) resulted from the approximate yet effective frequency-domain circuit analysis provide the wherewithal to increase modulation bandwidth up to 80% higher than the classic single-ended Class-E PA. This increased modulation bandwidth is required for the linearity improvement in the EER/ET transmitters. The modified output load network of the power-combining Class-E amplifier adopting three-harmonic terminations technique relaxes the design specifications for the additional filtering block typically required at the output stage of the transmitter chain. Qualitative agreements between simulation and measurement results for all four schemes were achieved where the ET technique was proven superior to the other schemes. When the PA is used within the ET scheme, an increase of average drain efficiency of as high as 40% with respect to the CW excitation was obtained for a multi-carrier input signal with 12 dB peak-to-average power ratio.