Arrangements for preventing electrical energy from lightning strikes against aircraft dissipating via aircraft fasteners 10 in an aircraft structure of composite materials in which a fastener 10 is covered with a layer of an insulating material 30 and a layer of a conductive material 32 is arranged to cover the insulating material 30 and extend over and beyond the lateral edges of the fastener 10, and preferential dielectric breakdown paths are provided at the edges of the conductive layer 32 distant from the fastener 10 so that in the event of a lightning strike electrical energy is not dissipated via the fastener 10, risking arcing and sparking, but instead from the edges of the conducting layer 32 to the underlying aircraft skin 12.