Following the increasing demand to make the creation and manipulation of 3D geometry simpler and more accessible, we introduce a modeling approach that allows even novice users to create sophisticated models in minutes. Our approach is based on the observation that in many modeling settings users create models which belong to a small set of model classes, such as humans or quadrupeds. The models within each class typically share a common component structure. Following this observation, we introduce a modeling system which utilizes this common component structure allowing users to create new models by shuffling interchangeable components between existing models. To enable shuffling, we develop a method for computing a compatible segmentation of input models into meaningful, interchangeable components. Using this segmentation our system lets users create new models with a few mouse clicks, in a fraction of the time required by previous composition techniques. We demonstrate that the shuffling paradigm allows for easy and fast creation of a rich geometric content.