Experiments are conducted to estimate the threshold for an all-or-none response. Threshold is defined to be a point above which 50% of the subjects will respond and below which 50% of the subjects will not respond. Examples are death, death in a fixed time period, shock, fibrillation, emesis. Staircase designs, in particular up-and-down trials, produce median (ED₅₀) estimates of given standard error with as few as one-fifth the number of subjects as the traditional designs with preset numbers of tests at each of several levels of stimulus. We discuss these estimates and their efficiency as well as procedures to estimate standard deviation and its use in designing up-and-down trials. The advantages in using several short series in factorial experiments are presented. Suggestions are given for minimizing the complications of sequential designs. Case studies indicate the efficiency of the design for various applications.