In this paper we propose a method denoted as ACELP for improving the speech quality of a Code-Excited-Linear-Predictive (CELP) codec at low bit rates by adaptation of the excitation codebook. The adaptive codebook consists of a set of basic excitation vectors which are adapted to an analysis speech frame by calculating optimum amplitude values. The amplitudes are quantized and encoded at a very low bit rate using a gain shape vector quantizer. The results of simulation experiments show that the mean squared error of CELP with an adaptive codebook is substantially lower than that of CELP with a fixed stochastic codebook. In informal listening tests the quality of the speech processed by the adaptive CELP scheme offered a reduced roughness and was less speaker dependent as with a conventionel CELP scheme.