This paper asks the question: are most species that are censused as rare in particular localities rare throughout most of their geographic ranges, or are they common in substantial portions of their ranges elsewhere? The first alternative is labeled suffusive rarity and the second diffusive rarity. To answer this and similar questions, rarity can be measured as the fraction of censuses from some locality (e.g., a quadrat) in which a species occurs (occurrence rarity), or the relative or absolute abundance of the species averaged over all censuses from some locality (abundance rarity). The question was analyzed for occurrence-rarity data from Australian terrestrial birds distributed over 1° (104-km2) quadrats. The great majority of species that are rare in a particular quadrat are not rare and are often common in a substantial number of other quadrats, i.e., these avian species are much closer to the diffusive than suffusive portion of the rarity continuum. The data also show that 1) the distribution of sizes of geographic ranges, whether breeding or total, is highly skewed, appearing exponential to more concave; 2) species are much rarer in their nonbreeding than breeding ranges; 3) more widespread species, whether breeding or total ranges are considered, tend to occur more rarely in a slightly but significantly greater fraction of their ranges; and 4) hawks and owls, typified by high abundance rarity, show occurrence rarity in a greater fraction of their ranges than the average nonraptorial species. Although continental birds may be especially predilected toward diffusive rarity, the present analysis points to identification of centers of abundance as major ways of preserving those species contributing most to recorded instances of rarity. Similar analyses with other kinds of organisms would be most welcome.