Small lightning flashes detected on Jupiter by Juno have shallow origins above the 2-bar level of Jupiter's atmosphere where temperatures are too low for liquid water to exist. Lightning flashes have been observed by a number of missions that visited or flew by Jupiter over the past several decades. Imagery led to a flash rate estimate of about 4 x 10(-3)flashes per square kilometre per year (refs.(1,2)). The spatial extent of Voyager flashes was estimated to be about 30 kilometres (half-width at half-maximum intensity, HWHM), but the camera was unlikely to have detected the dim outer edges of the flashes, given its weak response to the brightest spectral line of Jovian lightning emission, the 656.3-nanometre H alpha line of atomic hydrogen(1,3-6). The spatial resolution of some cameras allowed investigators to confirm 22 flashes with HWHM greater than 42 kilometres, and to estimate one with an HWHM of 37 to 45 kilometres (refs.(1,7-9)). These flashes, with optical energies comparable to terrestrial 'superbolts'-of (0.02-1.6) x 10(10) joules-have been interpreted as tracers of moist convection originating near the 5-bar level of Jupiter's atmosphere (assuming photon scattering from points beneath the clouds)(1-3,7,8,10-12). Previous observations of lightning have been limited by camera sensitivity, distance from Jupiter and long exposures (about 680 milliseconds to 85 seconds), meaning that some measurements were probably superimposed flashes reported as one(1,2,7,9,10,13). Here we report optical observations of lightning flashes by the Juno spacecraft with energies of approximately 10(5)-10(8) joules, flash durations as short as 5.4 milliseconds and inter-flash separations of tens of milliseconds, with typical terrestrial energies. The flash rate is about 6.1 x 10(-2)flashes per square kilometre per year, more than an order of magnitude greater than hitherto seen. Several flashes are of such small spatial extent that they must originate above the 2-bar level, where there is no liquid water(14,15). This implies that multiple mechanisms for generating lightning on Jupiter need to be considered for a full understanding of the planet's atmospheric convection and composition.