Modeling free surface water waves is difficult when waves are high (non-linear) and short (frequency dispersive). For flows without free surface overturning, depth-averaged models solve this issue by incorporating the free surface kinematic boundary condition in the model equations, the water depth being a new model variable. However, depite many attempts to built models with satisfactory properties (see e.g., Boussinesq (1877), Green and Naghdi. (1976), Bonneton et al., 2011), existing numerically robust models still suffer from inaccuracies when compared to the Euler equations of incompressible free surface flows. Recently, Clamond and Dutykh (2012) proposed a variational approach starting from Luke (1967)’s Lagrangian of water waves. By relaxing the Lagrangian and prescribing appropriate ans¨atze for the velocity components, they obtained a variety of existing models (e.g. the Serre–Green–Naghdi model) and create new models with improved performances. Here we push further their method by prescribing velocity ans¨atze that satisfy the three-dimensional incompressibility condition. The minimum principle applied to the resulting Lagrangian yields a one-parameter family of governing equations that resemble the Serre–Green–Naghdi model but with enhanced properties. In particular, the linearized dispersion relation approches well Euler’s one (see Figure below), but other desirable properties will be exhibited at the conference, like the nice behaviour of Stokes’ second harmonic, existence of travelling waves including a family of solitary waves, etc.