Electron-phonon interactions appear to explain some of, but not all, the features of the dispersive kinks in recently observed by angle-resolved photoemission spectroscopy. The remaining anomalies have led to suggestions that magnon, and not phonon, interactions are involved. If one abandons the effective-medium approximation and replaces it with dopant-centred filamentary percolation, a picture emerges that is consistent not only with the photoemission experiments but also with tunnelling, infrared and neutron scattering data.