  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 +/- 0.038 +/- 0.024 Mjup and R_b = 1.044 +/- 0.029 +/- 0.015 Rjup. It
has a low equilibrium temperature of 1280 +/- 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.
