In their study of the unitary dual for complex reductive groups, Barbasch and Vogan gave a characterisation of the unipotent Arthur packets using a microlocal invariant called the wavefront set. In this talk I will present joint results with Maxim Gurevich in which we pursue this approach for classical p-adic groups. We find that the packets defined microlocally are a union of Arthur packets which can be characterised by a surprising spectral property, namely the existence of an invariant vector for a (not necessarily hyperspecial) maximal compact subgroup.