In the Neotropics, most plants depend on animals for pollination. Solitary bees are the most important vectors, and among them members of the tribe Centridini depend on oil from flowers (mainly Malpighiaceae) to feed their larvae. This specialized relationship within 'the smallest of all worlds' (a whole pollination network) could result in a 'tiny world' different from the whole system. This 'tiny world' would have higher nestedness, shorter path lengths, lower modularity and higher resilience if compared with the whole pollination network. In the present study, we contrasted a network of oil-flowers and their visitors from a Brazilian steppe ('caatinga') to whole pollination networks from all over the world. A network approach was used to measure network structure and, finally, to test fragility. The oil-flower network studied was more nested (NODF = 0·84, N = 0·96) than all of the whole pollination networks studied. Average path lengths in the two-mode network were shorter (one node, both for bee and plant one-mode network projections) and modularity was lower (M = 0·22 and four modules) than in all of the whole pollination networks. Extinctions had no or small effects on the network structure, with an average change in nestedness smaller than 2% in most of the cases studied; and only two species caused coextinctions. The higher the degree of the removed species, the stronger the effect and the higher the probability of a decrease in nestedness. We conclude that the oil-flower subweb is more cohesive and resilient than whole pollination networks. Therefore, the Malpighiaceae have a robust pollination service in the Neotropics. Our findings reinforce the hypothesis that each ecological service is in fact a mosaic of different subservices with a hierarchical structure ('webs within webs'). Theoretical and practical relevance: This paper goes one step further in the hypothesis of mutualistic modules, evidencing that ecosystem services may be a mosaic of subservices with different properties. Furthermore, this finding has important implications for service-oriented conservation programs, as their planning should take into account this hierarchical structure.