Multiferroic heteroepitaxial nanocomposite films of BaTiO3 and CoFe2O4 (CFO) have been grown by pulsed laser deposition employing alternating ablation of two ceramic targets. Films grown at temperatures between 650 degrees C and 710 degrees C contain columnar CFO grains about 10-20 nm in diameter embedded in a BaTiO3 matrix. The very strong vertical compression of these grains causes large perpendicular magnetic anisotropy. Post-growth annealing treatments above the growth temperature gradually release the compression. This allows one to tune the stress-induced magnetic anisotropy. Additionally, annealing leads to substantial enhancement of the saturation magnetization M-S. Since M-S of a pure CFO film remains unchanged by a similar annealing procedure, M-S is proposed to depend on the volume fraction of the obtained CFO phase. We suggest that M-S can be utilized to monitor the degree of phase separation in nanocomposite films. (C) 2013 AIP Publishing LLC.