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Elves are observed as expanding rings of light in the UV and visible optical bands. They are produced when electromagnetic pulses from lightning discharges interact with the lower parts of the ionosphere. Elves are well known to be associated with high peak current lightning discharges. Here, we use data from the Modular Multi‐spectral Imaging Array (MMIA) of the Atmosphere‐Space Interactions Monitor (ASIM), and search for observations of Elves when high peak current lightning discharges are detected by Vaisala's Global Lightning Detection network GLD360. We present two groups of events; high peak current detections associated with Elves and high peak current detections not associated with Elves. To understand why some current pulses with high peak currents do not produce observable Elves, we investigate and compare the lightning activity occurring before these two types of events, in terms of both the number of lightning discharges detected by GLD360 and the peak currents of the preceding discharges. Our results, using data from GLD360, suggest that current pulses with peak currents above |120| kA tend to produce Elves nearly always, regardless of the preceding lightning activity. For current pulses with peak currents between |70| and |120| kA, the number of observed Elves might be affected by the preceding lightning activity, or is the result of the characteristics of the storm cells that produce the Elve. Plain Language Summary: There are many different phenomena that occur above active thunderstorms. Among these phenomena are Elves, which are observed as expanding rings of light (in UV and visible light) that are produced when powerful lightning pulses interact with the ionosphere at altitudes around 90 km. Elves are produced by strong electromagnetic waves from lightning pulses. We explore two sets of events in this study; strong lightning pulses that produce Elves, and strong lightning pulses that do not produce Elves. To understand why some strong pulses do not produce Elves, we investigate the lightning activity occurring before these events. We find that for lightning pulses with peak currents between |70| and |120| kA, the preceding lightning activity may affect whether an Elve is produced or not. Key Points: We present two types of events; high peak current lightning associated with Elves, and high peak current lightning not associated with ElvesFor peak currents >120 kA the probability of producing an Elve is more than 95%For peak currents between 70 and 120 kA, previous lightning activity may influence whether an Elve is produced or not [ABSTRACT FROM AUTHOR]