The first discovery of the appendages belonging to the Bradoriida s.str. Arthropoda - generally supposed to have been ostracodes until now - is reported in Kunmingella from the early Cambrian soft-bodied `Chengjiang' Lagerstatte of China. Although this evidence does not particularly clarify the affinities of Kunmingella within the Arthropoda, it does demonstrate that this genus, and by implication other taxonomically allied bradoriids in general, are neither ostracode, crustacean s.str. nor closely related to the Phosphatocopida (also conventionally classed as ostracodes). This has far-reaching implications for the stratigraphical distribution and evolution of the Class Ostracoda: that much (all?) of their Cambrian record is most likely spurious. The discovery also endorses the fact that arthropod radiation involved several different types of convergently bivalved groups.