Dropping the shallow-atmosphere approximation implies for energetic consistency to also drop the "traditional approximation" where some components of the Coriolis force are neglected (White & Bromley, 1995). This yields either the full (non-hydrostatic) compressible Euler equations or the quasi-hydrostatic equations (QHE). We are currently extending LMD-Z (latitude-longitude grid) to solve the QHE. The complete Coriolis term presents challenges regarding the discrete conservation of enstrophy.