Avalanche noise measurements have been performed on a range of homojunction GaAs p(+)-i-n(+) and n(+)-i-p(+) diodes with "i" region widths, w from 2.61 to 0.05 mu m. The results show that for w less than or equal to 1 mu m the dependence of excess noise factor F on multiplication does not follow the well-established continuous noise theory of McIntyre [1], Instead, a decreasing noise factor is observed as w decreases for a constant multiplication. This reduction in F occurs for both electron and hole initiated multiplication in the thinner w structures even though the ionization coefficient ratio is close to unity. The dead-space, the minimum distance a carrier must travel to gain the ionization threshold energy, becomes increasingly important in these thinner structures and largely accounts for the reduction in noise,