The propagation of internal Alfvén-inertio-acoustic gravity waves in a perfectly electrically conducting, stratified, inviscid, non-isothermal, rotating atmosphere permeated by a non-uniform magnetic field is investigated. These waves exhibit singular properties at the critical levels at which the magnetic field and the sound velocity are such that \[ (\omega^2 - S^2)\{(c^2+V^2)\omega^2-c^2S^2\}-(c^2+V^2)\overline{R}^2=0, \] where ω is the frequency of the waves, $S = kV_x + lV_y,\overline{R} = 2\Omega_z\omega$, Vx and Vy are the x and y components of the Alfvén velocity, k and l are the corresponding wavenumbers and c is the sonic velocity. These levels act like valves which permit waves to penetrate them from one side only and absorb them when they propagate from the other side. In contrast to the incompressible results of Acheson (1972), we show that the valve effect in compressible flow no longer requires the presence of non-zero components of rotation in the plane normal to the direction in which the medium varies. We find that the compressibility increases the probability of a valve effect and so increases the capacity of a hydromagnetic wave to propagate across a field line, rather than being absorbed at some critical level.