A compilation is made of the largest and second-largest magnetic-storm-maximum intensities, −Dst₁ and −Dst₂, for solar cycles 14–24 (1902–2016) by sampling Oulu Dcx for cycles 19–24, using published −Dst_m values for 4 intense storms in cycles 14, 15, and 18 (1903, 1909, 1921, 1946), and calculating 15 new storm-maximum −Dst_m values (reported here) for cycles 14–18. Three different models are fitted to the cycle-ranked −Dst₁ and −Dst₂ values using a maximum-likelihood algorithm: A Gumbel model, an unconstrained Generalized-Extreme-Value model, and a Weibull model constrained to have a physically justified maximum storm intensity of −Dst_m = 2500 nT. All three models are good descriptions of the data. Since the best model is not clearly revealed with standard statistical tests, inference is precluded of the source process giving rise to storm-maximum −Dst_m values. Of the three candidate models, the constrained Weibull gives the lowest superstorm occurrence probabilities. Using the compiled data and the constrained Weibull model, a once-per-century storm intensity is estimated to be −Dst₁ = 663 nT, with a bootstrap 68% confidence interval of [497, 694] nT. Similarly, the probability that a future storm will have an intensity exceeding that of the March 1989 superstorm, −Dst_m > 565 nT, is 0.246 per cycle with a 68% confidence interval of [0.140, 0.311] per cycle. Noting (possibly slight) ambiguity in the rankings of storm intensities, using the same methods, but storms more intense than those identified for cycles 14–16, would yield a higher once-per-century intensity and a higher probability for a −Dst_m > 565 nT storm.