Self-interference (SI) significantly limits the performance of full-duplex (FD) radio devices if not properly cancelled. State-of-the-art SI cancellation (SIC) techniques at the receive chain implicitly set an upper bound on the transmit power of the device. This paper starts from this observation and proposes a transmit beamforming design for FD multiple-antenna radios that: i) leverages the inherent SIC capabilities at the receiver and the channel state information; and ii) exploits the potential of multiple antennas in terms of spatial SIC. The proposed solution not only maximizes the throughput while complying with the SIC requirements of the FD device, but also enjoys a very low complexity that allows it to outperform state-of-the-art counterparts in terms of processing time and power requirements. Numerical results show that our transmit beamforming design achieves significant gains with respect to applying zero-forcing to the SI channel when the number of transmit antennas is small to moderate, which makes it particularly appealing for FD small-cell base stations.