Analysis of archival data from the BeppoSAX Wide Field Cameras has yielded further detections of superbursts. Remarkably, several are from a persistent low-mass X-ray binary (LMXB) that radiates within a few tens of percent of the Eddington limit, in contrast to all other superbursts detected with BeppoSAX and RXTE which are from LMXBs radiating between 0.1 and 0.25 times Eddington. These data provide important constraints for superburst models which are based on unstable carbon burning in the top 100 m of the neutron star. Another new result concerns evidence that stable helium burning is an important process in producing the fuel for such carbon shell flashes.