Low amplitude rhythmic discharges (RDs) closely associated in time and in spatial distribution to inter-ictal epileptiform discharges are not seen in scalp EEGs of patients with non-periodic focal epileptiform discharges (NPEDs) but they are unexpectedly common in patients with periodic lateralized epileptiform discharges (PLEDs). A classification of PLEDs into PLEDs Proper (PLEDs without RDs), and PLEDs Plus (PLEDs with RDs) is proposed. Such a classification is useful for an easier appreciation of PLEDs' pleomorphism. It underscores the changing periodicity of PLEDs and allows for a more inclusive definition of the phenomenon than the one reported by the literature. It also emphasizes the importance of recognizing RDs in scalp EEGs as transitional anomalies intercalated between inter-ictal PLEDs and ictal seizure discharges, analogous to those observed by Ralston in animal models. Indeed, the occurrence of recorded seizures is higher in patients with PLEDs Plus than in those with PLEDs Proper or NPEDs.