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Introduction. The growth in the volume of information transmitted through communication channels leads to their significant congestion. Almost all methods conventionally used to increase the data transfer rate in given frequency bands have been exhausted. In this regard, it is of interest to use new approaches aimed at improving the spectral efficiency of radio engineering and telecommunication systems by applying optimal signals that make it possible to use the bandwidth reserves of transmission channels given by Shannon's theory.Aim. Improvement of the spectral efficiency of digital messaging systems by using signals with a compact spectrum and increased volume of the channel alphabet at the same time as minimizing energy losses.Materials and methods. When searching for optimal signals, the mathematical apparatus of communication theory and functional analysis, as well as the methods of calculus of variations, were used. The evaluation of bit error rate performance of the obtained optimal signals transmitted in a channel with additive white Gaussian noise was performed in the MatLab environment. Results. It was established that, in a channel with additive white Gaussian noise, optimal signals with a signal constellation size of 64 in the case of quadrature amplitude-phase modulation provide an energy gain of more than 1 dB relative to signals obtained by narrowband filtering under the conditions of uncontrolled intersymbol interference. Optimal signals were shown to provide for an energy gain of 4.9 dB with respect to signals based on narrow-band filtering at a fixed spectral efficiency of 7 (bit/s)/Hz.Conclusion. The paper proposes a method for improving the spectral efficiency of quadrature signals with amplitudephase modulation, based on the use of optimal pulse shapes obtained as a result of solving an optimization problem. The optimization problem was solved according to the criterion of minimizing out-of-band emissions with the constraint on bit error rate performance in case of amplitude-phase modulation. The energy and spectral efficiency of signals with optimal pulse shapes and signals based on narrow-band filtering were compared.