The avalanche-multiplication and noise characteristics of a series of thin (0.05 mu m < w < 1 mu m) p(+)-i-n(+) GaAs and Al0.3Ga0.7As diodes have been measured. According to the widely used theory of McIntyre, the lowest excess-noise factor should be obtained with materials that have a small ratio of ionisation coefficients, k = beta/alpha, where alpha is the ionisation coefficient of the initiating carrier. It has been found, however, that in thin avalanche regions, < 1 mu m, the assumptions of McIntyre's noise theory become increasingly invalid and low noise factors can be achieved even when k is of the order of 1. In such thin devices, the dead space becomes a significant fraction of w, reducing the randomness in ionisation path length and hence the noise.