In this work we analyse the relation between hierarchical distance-based clustering and the concepts that can be obtained from the hierarchy by generalisation. Many inconsistencies may arise, because the distance and the conceptual generalisation operator are usually incompatible. To overcome this, we propose an algorithm which integrates distance-based and conceptual clustering. The new dendrograms can show when an element has been integrated to the cluster because it is near in the metric space or because it is covered by the concept. In this way, the new clustering can differ from the original one but the metric traceability is clear. We introduce three different levels of agreement between the clustering hierarchy obtained from the linkage distance and the new hierarchy, and we define properties these generalisation operators should satisfy in order to produce distance-consistent dendrograms.