Several supercell storms have occurred within the region in which the Oklahoma Lightning Mapping Array (OKLMA) maps all three spatial dimensions of lightning. These storms span much of the supercell spectrum -- from non-tornadic storms to storms that produced strong tornadoes and from low-precipitation to heavy-precipitation morphologies. As noted by several studies, supercell storms tend to have much larger flash rates than ordinary isolated thunderstorms; maximum rates are typically hundreds of flashes per minute, even when considering only flashes that produce at least ten mapped points per flash. However, the OKLMA indicates that most of the flashes occurring within the main body of the storm during periods of high flash rates have quite small spatial extents, many with a long dimension of 5 km or less. Not usually included in these flash rates are a large number that appear to be isolated points (sometimes called singletons), each failing criteria of distance or time for associating it with other points in a flash. Often determining whether these isolated points are artifacts of the OKLMA is difficult, but in the overshooting top, they present a coherent pattern that appears plausible. They are distributed throughout a cap having horizontal dimensions comparable to that of the overshooting top and sitting near or on the upper surface. They occur continually, though they are too far apart in time or space to be associated in a flash with each other. A comparison with high-resolution reflectivity data for one storm observed by the two mobile 5-cm wavelength SMART-R radars shows that these isolated points were most concentrated near the top of the 40 dBZ echo in the overshooting turret, but some occurred higher, in regions of small reflectivity or just above the overshooting top. These points may be similar to the continual lightning noted by Bill Taylor in the upper region of a severe storm in the early 1980s.