Application of the exponential power estimation (EPE) technique to develop computationally simple algorithms for adapting the quantiser and predictor of an adaptive differential pulse code modulation (ADPCM) system has been investigated. Performance of this EPE-based ADPCM system (E-ADPCM) has been studied for first order Gauss-Markov and real speech inputs (three sentences) under different channel conditions (noise-free and noisy channels), using a Gaussian non-uniform quantiser at the bit-rate of 16 kilobits per second (kbit/s). Performance of the proposed ADPCM has been compared with that of two conventional ADPCM systems. The E-ADPCM has a superior performance to the conventional systems considered, with a computational advantage of (3N+ B + 1) multiplications (Nbeing the predictor order andB, the number of bits per sample used for quantising the prediction error) and one division per iteration compared with the first system and (B+ 1) multiplications over the second system, at the cost of one exponentiation.