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We investigate the effect of biaxial strain on the switching of ferroelectric thin films. The strain state of epitaxial PbZr _0.52 Ti _0.48 O _3 films is controlled directly and reversibly by the use of piezoelectric Pb(Mg _1/3 Nb _2/3 ) _0.72 Ti _0.28 O _3 (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.