We will describe the development of a non-hydrostatic dynamical core for the Department of Energy's (DOE) Accelerated Climate Model for Energy (ACME) program. Our non-hydrostatic core is being developed in ACME's verison of HOMME and shares many of the underlying computational kernels including full support for variable resolution meshes. We use the Laprise mass coordinate formulation of the equations with the shallow atmosphere approximation. The Laprise system supports both hydrostatic and non-hydrostatic formulations. The hydrostastic formulation is nearly identical to ACME's existing hydrostatic dynamical core and the nonhydrostatic formulation adds two additional prognostic variables (vertical velocity and geopotential height). The discretization relies on mimetic methods: spectral finite elements in the horizontal and finite differences in the vertical, with both vertically Lagrangian and Eulerian options. We use a horizontally-explicit vertically-implicit (HEVI) IMEX approach for the time discretization. We introduce a moist  potential temperature as a prognostic variable, and formulate the equations so that total energy are conserved through the use of mimetic discretizations. Initial results will be presented from several of the DCMIP idealized test cases.