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Extreme precipitation often persists for multiple days with variable duration but has usually been examined at fixed duration. Here we show that considering extreme persistent precipitation by complete event with variable duration, rather than a fixed temporal period, is a necessary metric to account for the complexity of changing precipitation. Observed global mean annual-maximum precipitation is significantly stronger (49.5%) for persistent extremes than daily extremes. However, both globally observed and modeled rates of relative increases are lower for persistent extremes compared to daily extremes, especially for Southern Hemisphere and large regions in the 0-45 degrees N latitude band. Climate models also show significant differences in the magnitude and partly even the sign of local mean changes between daily and persistent extremes in global warming projections. Changes in extreme precipitation therefore are more complex than previously reported, and extreme precipitation events with varying duration should be taken into account for future climate change assessments.