We investigate the effect of biaxial strain on the switching of ferroelectric thin films. The strain state of epitaxial PbZr0.52Ti0.48O3 films is controlled directly and reversibly by the use of piezoelectric Pb(Mg1/3Nb2/3)0.72Ti0.28O3 (001) substrates. At small external electric fields, the films show switching characteristics consistent with a creep-like domain wall motion. In this regime, we find a huge decrease of the switching time under compressive strain. For larger external electric fields, the domain wall motion is in a depinning regime. The effect of compressive strain is more moderate in this region and shows a reduction in the switching kinetics.