Differential privacy is often studied under two different models of neighboring datasets: the add-remove model and the swap model. While the swap model is frequently used in the academic literature to simplify analysis, many practical applications rely on the more conservative add-remove model, where obtaining tight results can be difficult. Here, we study the problem of one-dimensional mean estimation under the add-remove model. We propose a new algorithm and show that it is min-max optimal, achieving the best po…