Reflection high-energy electron diffraction (RHEED) has been used to monitor the growth of La1.85Sr0.15CuOx (LSCO) thin films on (100) SrTiO3 substrates by pulsed laser deposition. The films are grown using a combination of pulsed molecular oxygen and a continuous source of atomic oxygen, with the average background pressure maintained as low as 1 mTorr. The RHEED pattern is sharp and streaky, and the intensity of the specular beam oscillates during the deposition, indicating a two-dimensional layer-by-layer epitaxial growth. The film thickness measured by x-ray small-angle interference is consistent with the thickness determined by the RHEED oscillation period with a growth unit of half a unit cell. Thin films of YBa2Cu3O7-δ (YBCO) with good RHEED oscillations have also been grown under similar oxygenation conditions. The low-pressure-grown LSCO and YBCO films are superconducting, with zero-resistance temperatures of 15 and 80 K, respectively.