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This study focuses on the development of low-resolution symbol-level precoding techniques for multiuser MIMO downlink systems with PSK modulation. While for QPSK the established minimum symbol error probability criterion is used, a criterion for PSK modulation, in general, is proposed based on the minimum union-bound symbol-error probability. Based on these criteria different low-resolution precoding approaches are proposed. First, suboptimal solutions are computed via a partial greedy search method. Then the suboptimal solutions are utilized as initialization for a novel branch-and-bound algorithm that can exploit knowledge of the system's quality-of-service demands. Different than existing branch-and-bound approaches the proposed quality-of-service branch-and-bound method searches for a solution that attains a target symbol-error probability while going in the direction of the global optimal solution. In this sense, the proposed branch-and-bound method allows for tunable complexity performance trade-offs. Numerical results confirm that the proposed quality-of-service branch-and-bound algorithm yields reduced symbol-error probability with significantly smaller computational complexity than other state-of-the-art branch-and-bound designs.