Summary: Variational principles have become quite popular in the design of surfaces. The idea is to consider a class of surfaces having more degrees of freedom than are necessary to fulfill the constraints (e.g. interpolation or boundary conditions). The remaining degrees of freedom are set by minimizing a fairness functional. The choice of the ‘right’ fairness functional is a crucial step. In this paper we describe a systematic approach for choosing an appropriate fairness functional that produces high quality surfaces and which allows the solution of the optimization problem in a reasonable amount of time.