One possibility to construct heavy tail distributions is to directly manipulate a standard Gaussian random variable by means of transformations which satisfy certain conditions. This approach dates back to Tukey (1960) who introduces the popular H-transformation. Alternatively, the K-transformation of MacGillivray and Cannon (1997) or the J-transformation of Fischer and Klein (2004) may be used. Recently, Klein and Fischer (2006) proposed a very general power kurtosis transformation which includes the above-mentioned transformations as special cases. Unfortunately, their transformation requires an infinite number of unknown parameters to be estimated. In contrast, we introduce a very simple method to construct flexible kurtosis transformations. In particular, manageable ``superstructures'' are suggested in order to statistically discriminate between H-, J- and K-distributions (associated to H-, J- and K-transformations).