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This paper investigates peak-to-average power ratio (PAR) reduction with constrained transmit power for spatially precoded downlink transmission, based on orthogonal frequency-division multiplexing (OFDM). We generalize the concept of multiuser Tomlinson-Harashima (T-H) precoding and propose a nonlinear spatial precoder, termed a complex sphere precoder (CSP), which has the same throughput and error performance as the T-H precoder, but achieves both a low PAR and low average transmit power. Our study shows that a sequential CSP over individual tones achieves a significant PAR reduction while requiring a moderate transmit power increase. The suboptimal per-tone lattice search constitutes a good compromise between performance and complexity.