The growth of the Intemet has revitalised research on the integration of heterogeneous information sources. Integration efforts face a trade off between interoperability and heterogeneity. Important integration obstacles arise from the differences in the underlying ontologies of the various sources. In this paper we investigate the impediments to integration, focussing on ontologies. In particular, we present a classification of ontology mismatches (distinguishing conceptualisation mismatches and explication mismatches as its main categories), and discuss how each of the mismatch types can be dealt with. The idea is that knowing which ontology mismatches are difficult to deal with may contribute to finding a balance between heterogeneity and interoperability.