Thin superconducting films of YBa2Cu3O7−xwere deposited onto (100) SrTiO3substrates at 750 °C in 100 and 200 mTorr of O2, by ArF excimer laser ablation. The as‐deposited films were strongly oriented with thecaxis perpendicular to the surface when they were cooled to room temperature in oxygen. The highest values of transport critical current density (Jc≳105A/cm2below 80 K) were observed in films cooled in flowing O2. We find that, in all films,Jcfollows a power law (1−T/Tc)nwithn≊2, near the critical temperature,Tc, whenTcis defined as the temperature at whichJc=0. It appears that this behavior is governed by the short coherence lengths in this high‐Tcmaterial, as suggested by G. Deutscher and K. A. Mu¨ller [Phys. Rev. Lett.59, 1745 (1987)], and not by the specific nature of the large‐scale structure of the films.