A signal power associated with a signal received in a current time period is determined. The determined signal power is combined with a predicted effective interference to form a predicted signal-to-interference indicator. The predicted signal-to-interference indicator is compared to a target signal-to-interference indicator. One or more transmit power control commands are generated based on the comparison. In one example embodiment, the predicted effective interference is based on an effective interference estimated for a previous time period. In another example embodiment, the predicted effective interference is based on interference contributions estimated in a current time period and a predicted interference cancellation efficiency. The predicted interference cancellation efficiency is based on the estimated interference cancellation efficiency for a previous time period. The technology is particularly useful in receivers that use interference cancellation and achieves excellent transmit power control performance both in terms of accuracy and speed.