In this paper we first consider conventional multichannel systems with fixed-power variable-rate transmission of independent data streams as a function of channel variations. In the conventional systems, no data is transmitted through the channels whose received signal strength is below a certain cut off threshold. We then propose a new hybrid adaptive modulation and diversity scheme for multi-channel transmission systems. The proposed hybrid scheme attempts to increase the overall spectral efficiency by (i) transmitting redundantly information symbols through the deeply faded channels that are not to be used in conventional multi-channel systems and then (ii) diversity combining these signals at the receiver end. We calculate the spectral efficiency of the newly proposed hybrid scheme and compare it to the spectral efficiency of (i) the conventional system and (ii) a benchmark optimal but complex joint adaptive and diversity scheme that maximizes the overall spectral efficiency. We show, with the help of some selected numerical examples, that the proposed hybrid scheme offers almost the same spectral efficiency as the optimal scheme with much reduced complexity.