Adaptive transform coding using the discrete cosine transform for monochrome pictures is considered. Selecting which coefficients to transmit and with how many bits involves an estimate of each coefficient's energy. Dividing the image of 256 lines, 256 pels/line into blocks of 16 × 16 pels, we consider two estimation methods for the bit allocation process. One method involves the mean energy of each coefficient, while the other is an approximation to this method, called Energy Distribution Logarithmic Model, that drastically reduces the amount of side information that must be transmitted. To this we add an adaptive coefficient selection procedure based on the energy of three neighbouring coefficients. Performing the experiments by means of computer simulation we were able to achieve an average of 0.55 bits/pel for a recovered image having a mean square error of 0.1%.