This paper investigates the problem of the interference among multiple simultaneous transmissions in the downlink channel of a multiantenna wireless system. A symbol-level precoding scheme is considered, in order to exploit the multiuser interference and transform it into useful power at the receiver side, through a joint utilization of the data information and the channel state information. In this context, this paper presents novel strategies that exploit the potential of symbol-level precoding to control the per-antenna instantaneous transmit power. In particular, the power peaks among the transmitting antennas and the instantaneous power imbalances across the different transmitted streams are minimized. These objectives are particularly relevant with respect to the nonlinear amplitude and phase distortions induced by the per-antenna amplifiers, which are important sources of performance degradation in practical systems. More specifically, this paper proposes two different symbol-level precoding approaches. The first approach performs a weighted per-antenna power minimization, under quality-of-service constraints and under a lower bound constraint on the per-antenna transmit power. The second strategy performs a minimization of the spatial peak-to-average power ratio, evaluated among the transmitting antennas. Numerical results are presented in a comparative fashion to show the effectiveness of the proposed techniques, which outperform the state-of-the-art symbol-level precoding schemes in terms of spatial peak-to-average power ratio, spatial dynamic range, and symbol error rate over nonlinear channels.