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The formation of secondary ice in clouds, that is, ice particles that are created at temperatures above the limit for homogeneous freezing without the direct involvement of a heterogeneous ice nucleus, is one of the longest-standing puzzles in cloud physics. Here, we present comprehensive laboratory investigations on the formation of small ice particles upon the freezing of drizzle-sized cloud droplets levitated in an electrodynamic balance. Four different categories of secondary ice formation (bubble bursting, jetting, cracking, and breakup) could be detected, and their respective frequencies of occurrence as a function of temperature and droplet size are given. We find that bubble bursting occurs more often than droplet splitting. While we do not observe the shattering of droplets into many large fragments, we find that the average number of small secondary ice particles released during freezing is strongly dependent on droplet size and may well exceed unity for droplets larger than 300 mu m in diameter. This leaves droplet fragmentation as an important secondary ice process effective at temperatures around -10 degrees C in clouds where large drizzle droplets are present.