Composite thin films of 60 wt% Ba0.6Sr0.4TiO3 and 40 wt% MgO were produced by Pulsed Laser Deposition. The biaxial texture of the BST component on the MgO substrate has been established with XRD. All as-deposited films had an enlarged BST out-of-plane lattice parameter. A more relaxed lattice constant as well as higher degree of texture has been obtained in the films deposited at higher temperature and lower deposition rate. Post-deposition annealing in flowing oxygen results in a further relaxation and alignment of the BST lattice. The as-deposited films were not tunable at room temperature. The greatest dielectric tuning was achieved in films annealed at 1200 °C. The observed difference in tunability for the films annealed at different temperatures may result from a spatial redistribution of BST material on the substrate surface during annealing.