For many years it has been debated whether the quiet solar corona is heated by nanoflares and microflares or by magnetic waves. In this paper TRACE data of events with energies in the range 1023-1026 ergs are investigated. A new stable and objective statistical technique is proposed to determine the index, -γ, of a power-law relation between the frequency of the events and their energy. We find that γ is highly dependent on the form of the line-of-sight depth assumed to determine the event energies. If a constant line-of-sight depth is assumed, then γ lies between 2.4 and 2.6; however, if a line-of-sight depth of the form (Ae/k2)1/2 is assumed, where Ae is event area and k is a constant, then γ lies between 2.0 and 2.1. In all cases the value of γ is greater than 2 and therefore implies that the events with the lowest energies dominate the heating of the quiet solar corona. Moreover, there are strong indications that there is insufficient energy from events with nanoflare energies (i.e., energies in the range 1024-1027 ergs) to explain the total energy losses in the quiet corona. However, our results do not rule out the possibility that events with picoflare energies (i.e., energies in the range 1021-1024 ergs) heat the quiet corona. From analysis of the spatial distribution of the events, we find that events are mainly confined to regions with the brightest EUV emission, which are presumably the regions connected to the strongest magnetic fields. Indeed, just 16% of the quiet corona possesses such events.