Our research aimed at investigating whether 8-to-12-year-old children spontaneously make the conventional implicature induced by ‘but’ -combined with ‘so’ and ‘nevertheless’- in ‘p but q’ sentences. We presented the children with stories ending with a ‘p but q’ sentence. They were instructed to indicate the ‘appropriate’ conclusion introduced by either ‘so’ or ‘nevertheless’. In addition, we measured children’s working memory (WM)-capacity in order to explore the possibility that making these inferences is effortful. Our results show that children do make the inferences to a certain extent but are sensitive to the content of the arguments. Whenever the p- or q-argument is an absurd argument (contrasted with a sensible argument), this argument almost always gets ignored in favor of the sensible argument, irrespective of the ‘appropriate’ conclusion ‘but’ directs the reader to. No reliable WM-effect was found. High WM-span children did not make the inference more often than low WM-span children.