Range size is a universal characteristic of every biological species, and is often assumed to affect diversification rate. There are strong theoretical arguments that large-ranged species should have higher rates of diversification. On the other hand, the observation that small-ranged species are often phylogenetically clustered might indicate high diversification of small-ranged species. This discrepancy between theory and the data may be caused by the fact that typical methods of data analysis do not account for range size changes during speciation. Here we use a cladogenetic state-dependent diversification model applied to mammals to show that range size changes during speciation are ubiquitous and small-ranged species indeed diversify generally slower, as theoretically expected. However, both range size and diversification are strongly influenced by idiosyncratic and spatially localized events, such as colonization of an archipelago or a mountain system, which often override the general pattern of range size evolution.