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In this paper, we analyze the performance of a multi-channel system with the conventional adaptive modulation (AM) and two hybrid schemes, the adaptive modulation with diversity combining (AMDC) and the adaptive modulation with power loading (AMPL), respectively. In order to achieve higher spectral efficiency and more efficient usage of channel resources under the total transmit power constraint and the required bit error rate (BER), the AMDC jointly uses discrete-rate adaptation and diversity combining scheme, and the AMPL jointly uses discrete-rate adaptation and sub-optimal discrete-power loading. We derive exact closed-form expressions of the performance of a multi-channel system with the conventional adaptive modulation (AM) and these hybrid schemes, in terms of the spectral efficiency, the average BER and the outage probability. We also analyze the impact of imperfect channel estimation on the error performance and validate our analytical results by simulations. Numerical results show that both the AMDC and the AMPL offer higher spectral efficiency than the conventional AM, assuming the perfect channel estimation. However, AMDC offers better performance and reliability than AMPL, under imperfect channel estimation with complex Gaussian error.