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The cumulative distribution function transform (CDFt) downscaling method has been used widely to provide local-scale information and bias correction to output from physical climate models. The CDFt approach is one from the category of statistical downscaling methods that operates via transformations between statistical distributions. Although numerous studies have demonstrated that such methods provide value overall, much less effort has focused on their performance with regard to values in the tails of distributions. We evaluate the performance of CDFt-generated tail values based on four distinct approaches, two native to CDFt and two of our own creation, in the context of a "Perfect Model" setting in which global climate model output is used as a proxy for both observational and model data. We find that the native CDFt approaches can have sub-optimal performance in the tails, particularly with regard to the maximum value. However, our alternative approaches provide substantial improvement.