Modern wireless systems are expected to support both communication and sensing, forming the foundation of Integrated Sensing and Communication (ISAC). Although many approaches have been proposed, practical and efficient solutions remain an open challenge. This work addresses this issue by constraining transmitted MIMO radar waveforms to finite-alphabet signals, which are better suited for power amplifiers and signal processing hardware. Under this setting, we investigate methods to jointly enhance communication and sensing performance. First, by exploiting the beampattern-invariance property, we reduce the computational complexity of an existing finite-alphabet waveform generation method and address its limitations to further improve performance. Furthermore, we propose beampattern-preserving schemes that embed communication data into radar waveforms without altering the beampattern, enabling practical ISAC implementation. Specifically, two information-encoding methods and a new precoding technique are introduced, together with an extension to multi-user scenarios based on time and code division. Simulation results demonstrate the trade-off between radar and communication performance.