A discussion of the evolution of the HE 12 (LP 02 ) field, and thus the role of the core in H E n -H 1 2 (LP 01 -LP 02 ) local-mode coupling for a tapered 'doubly-clad' lightguide as may be formed by the combination finite-cladding fibre and external medium (i.e. outer cladding) is presented. Consideration of more than one interface injects interesting novel features into the local-normalmode viewpoint: examination of the HE 12 lobe maximum and field evolution leads to the discovery of a core/cladding bounce phenomenon (related to an HE 12 leaky-mode property) as well as an intriguing coupling phase dependence.