The effect of the impact ionization dead space on avalanche multiplication and noise has been assessed for uniform p-i-n avalanche photodiodes. This has required the development of a new numerical technique. The well-established McIntyre theory of avalanche noise [IEEE Trans. Electron Devices ED-13, 164 (1966)], which neglects the ionization dead-space effect, has been shown to overestimate the excess noise factor. The implications of the dead-space effect, for ionization coefficient determination and the interpretation of measured excess noise factors, are discussed.