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Continuous sequential analysis is increasingly used for near real-time post-market drug and vaccine safety surveillance. We explore continuous sequential monitoring when the null cannot be rejected until a minimum number of adverse events have occurred. For fixed alpha, one can simultaneously increase the statistical power and reduce the expected time to signal. We also evaluate continuous sequential analysis with a delayed start until a certain sample size has been attained. This is only useful if the start of the surveillance is delayed for logistical reasons. Tables with exact critical values, statistical power and the average times to signal are provided.