We are interested in space-time refinement methods for linear wave propagation. In 1,2 , some stable numerical schemes using non-conforming grids in space and time have been proposed. These methods use a Lagrange multiplier to cope with the interface conditions. The choice of the discretization space of this additional unknown can be in some cases not trivial. In the present paper we propose an alternative method. The main new idea is to use different variational formulations in the fine and in the coarse grids. We present a time discretization that leads to the conservation of a discrete energy and provide a complete stability and error analysis in the case where the time step is twice smaller in one domain than in the other one.