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We compared alpha and recently proposed potential competitors (ordinal alpha, omega total, omega RT, omega h, GLB, and coefficient H) when they were used with non-normal continuous and discrete data. Results showed that for continuous data, estimation bias was large only when non-normality was severe, and non-normality was a problem with weak items. For Likert scales, other than omega h, most indices were acceptable with non-normal data, and four or more scale points were better. For exponentially distributed data, omega RT was quite robust for all distributions, and bias was generally larger for the binomial-beta distribution. An examination with large-scale surveys suggested that non-normality was not a critical issue as most of the actual items were at worst moderately non-normal.