We present calculations of magnetic field-dependent properties of magnetic shape memory (MSM) Heusler alloys by means of density functional theory calculations. The effects of an external magnetic field on structural properties are simulated by fixing the magnetic moments within the framework of the fixed spin moment (FSM) method. We calculate the binding surface as a function of the magnetic moment and the tetragonal distortion. For magnetizations of 10% below the equilibrium value, the energy of the martensitic L10 phase steeply increases leading to a relative stabilization of the L21 phase in a confined magnetization range. Calculations of the phonon dispersion in the direction [ξξ0]2π/a suggest that the instability at ξ≈1/3 disappears with decreasing magnetization, allowing a nearly stable spectrum in a small magnetization interval.