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This study deals with the evaluation and formulation of methods to improve the probabilistic quantification of maximum story drift demands for structural systems exposed to severe ground motions. The focus is on flexible structures that are prone to dynamic instability. The quantification of drift demands is based on the probability distribution of the maximum story drift over the height, for a given ground motion hazard level, which in this study is represented by the spectral acceleration at the first mode period of the building. Improvements in the probabilistic estimation of maximum story drift demands are illustrated with a nine-story, moment-resisting frame building exposed to a set of 40 ground motions. It is concluded that (1) the three-parameter LN distribution more rationally describes maximum story drifts at higher values of spectral acceleration; (2) statistically adding values to replace truncated data points provides better goodness-of-fit in maximum drift demand prediction when the structure is close to the onset of dynamic instability, and (3) the least-squares fitting of the LN distribution yields parameters that provide an improved fit compared to that from maximum likelihood estimation and the method of moments.