In this talk we will present a new method for deriving approximate equations for water waves. This method is based on a relaxed variational principle. In other words, the Lagrangian functional contains additional degrees of freedom. This formulation is particularly suitable for the construction of approximations since it allows more flexibility while preserving the variational structure. The advantages of this method will be illustrated on numerous examples in shallow and deep waters. Using thoroughly chosen constraints in various combinations, several model equations are derived, some being well-known, other being new. These models are studied analytically and exact traveling wave solutions are constructed when possible. The Hamiltonian structure is also unveiled whenever possible.