We present a formulation of an upper boundary condition for non-hydrostatic models that, by employing a second-order recursive filter in time to record a `memory' of the recent changes to the presssure perturbation and vertical velocity, enables an appropriate linear combination of these variables to be constrained so as to minimize the spurious reflection of gravity waves at a range of horizontal and vertical wavelengths and to at least partially absorb vertically-propagating acoustic waves. We will show preliminary results which illustrate the effectiveness of the proposed method in simulations involving propagating and topographically forced waves under various conditions of vertical stratification.