Before revision:  They are simple to compute, highly efficient, have excellent coverage properties in finite samples. They are also valid under weak identification (that is, if the jump in treatment probabilities at the threshold is small) and irrespective of whether the distribution of the running variableis continuous, discrete, or of some intermediate form .
After revision:  They are valid under a wide range of empirically relevant conditions in which existing CIs generally fail. These conditions include discrete running variables, donut designs, and weak identification. But our CS also perform favorably relative to existing CIs in the canonical setting with a continuous running variable, and can thus be used in all fuzzy regression discontinuity applications .