In this paper, three algorithms are proposed for rate maximization (RM) of transmitted data in multichannel (MC) communications, subject to joint constraints on available energy budget and tolerable degradation of service (DOS). Altogether referred to as the RM algorithms, they consist of the EADRM, the DADRM, and the fDADRM algorithms. Based on the rate-distortion optimization theory, closed-form expressions for optimally distributing the energy (for EADRM) or DOS (for DADRM and fDADRM ) among the subchannels (SC's) are derived, when the bit allocation is pre-specified. The specification of bit allocations is achieved by the use of the so-called eligible bit allocation matrix (EBAM), which is a function of the total data rate and the number of SC's. A greedy approach is adopted, where the total data rate is kept on raising until the relevant constraints can no longer be satisfied. While all three RM algorithms essentially generate identical maximum data rates, the fDADRM algorithm is much faster than the other two in computation. As compared to the result achievable by a single-channel communication scheme, the RM algorithms produce a much higher data rate for spectrally shaped channels.