We present high-precision photometry of three transits of the extrasolar planetary system WASP-2 , obtained by defocussing the telescope , and achieving point-to-point scatters of between 0.42 and 0.73 mmag . These data are modelled using the jktebop code , and taking into account the light from the recently-discovered faint star close to the system . The physical properties of the WASP-2 system are derived using tabulated predictions from five different sets of stellar evolutionary models , allowing both statistical and systematic errorbars to be specified . We find the mass and radius of the planet to be M _ { b } = 0.847 \pm 0.038 \pm 0.024 { M } _ { Jup } and R _ { b } = 1.044 \pm 0.029 \pm 0.015 { R } _ { Jup } . It has a low equilibrium temperature of 1280 \pm 21 K , in agreement with a recent finding that it does not have an atmospheric temperature inversion . The first of our transit datasets has a scatter of only 0.42 mmag with respect to the best-fitting light curve model , which to our knowledge is a record for ground-based observations of a transiting extrasolar planet .