A computationally efficient self-planning algorithm for adjusting base station transmit power in a LTE system on a cell-by-cell basis is presented. The aim of the algorithm is to improve the overall network spectral efficiency in the downlink by reducing the transmit power of specific cells to eliminate interference problems. The main driver of the algorithm is a new indicator that predicts the impact of changes in the transmit power of individual cells on the overall network Signal to Interference plus Noise Ratio (SINR) for the downlink. Algorithm assessment is carried out over a static system-level simulator implementing a live LTE network scenario. During assessment, the proposed algorithm is compared with a state-of-the-art self-planning algorithm based on the modification of antenna tilt angles. Results show that the proposed algorithm can improve both network coverage and capacity significantly compared to other automatic planning methods.