In the previous chapter we studied a range of common distributions. Many of these have been in existence for many years. Much of the development of distributional models has been based on seeking models with one or two parameters for fitting small samples of data. In these days of automated data collection one is often faced with very large data sets and the requirement for a small number of parameters can be relaxed. If there are a thousand observations it is probable that no two-parameter model will reasonably fit the data. We need to consider a larger catalogue of models and be able to build models that reflect the specific properties of the data being modelled. The objective of this chapter is to examine methods of building new models. In selecting approaches to be discussed, two considerations have been paramount. First, the models generated have structures that are likely to be useful to the practitioner. Thus we will be concerned with the forms of “model carpentry” that give commonly occurring tail shapes and meaningful parameters. Second, if the data comes from the given type of model it should be readily identified and validated. These two requirements put some realistic bounds on the types of model that ought to be considered and on the methods for constructing them. The models in the previous chapter provide a set of basic building blocks. In this chapter we therefore concentrate on how such simple components can be modified and combined to construct practical useful models.