Techniques for controlling the transmit power for a number of data streams in a wireless multi-channel (e.g., MIMO) communication system. In one method, a number of received symbol streams are initially processed in accordance with a particular (e.g., CCMI, CCMI-SC, MMSE, or MMSE-SC) receiver processing technique to provide a number of detected data streams. The post-detection SNRs of the detected data streams are estimated, and each SNR that exceeds a setpoint is identified. This setpoint may correspond to (1) the SNR needed to achieve the maximum allowed spectral efficiency or (2) the target SNR needed to achieve a specified spectral efficiency. A new (or adjusted) transmit power for each detected data stream associated with a post-detection SNR that exceeds the setpoint is determined and used for the data stream. Different power control schemes are provided for different classes of receiver processing techniques with different characteristics.