MgB2 thin films were cold grown on sapphire substrates by pulsed laser deposition followed by postannealing in mixed, reducing gas, Mg rich, Zr gettered, environments (pO2∼10-24 atm) at 750 and 950 °C. The films had Tc in the range 29–34 K, Jc (20 K, H=0) in the range 3×104–3×105 A cm-2, and irreversibility fields H* at 20 K of 4–6.2 T. An inverse correlation was found between Tc and H*. The films had grain sizes of ∼0.1–1 μm and a strong biaxial alignment was observed in the 950 °C annealed film. (111) oriented MgO was also observed. Mg coating of films during crystallization appeared to improve film Tc. © 2001 American Institute of Physics.