The recently approved NASA K2 mission has the potential to multiply by an order of magnitude the number of short-period transiting planets found by Kepler around bright and low-mass stars, and to revolutionise our understanding of stellar variability in open clusters. However, the data processing is made more challenging by the reduced pointing accuracy of the satellite, which has only two functioning reaction wheels. We present a new method to extract precise light curves from K2 data, combining list-driven, soft-edged aperture photometry with a star-by-star correction of systematic effects associated with the drift in the roll-angle of the satellite about its boresight. The systematics are modelled simultaneously with the stars intrinsic variability using a semi-parametric Gaussian process model. We test this method on a week of data collected during an engineering test in January 2014, perform checks to verify that our method does not alter intrinsic variability signals, and compute the precision as a function of magnitude on long-cadence (30-min) and planetary transit (2.5-hour) timescales. In both cases, we reach photometric precisions close to the precision reached during the nominal Kepler mission for stars fainter than 12th magnitude, and between 40 and 80 parts per million for brighter stars. These results confirm the bright prospects for planet detection and characterisation, asteroseismology and stellar variability studies with K2. Finally, we perform a basic transit search on the light curves, detecting 2 bona fide transit-like events, 7 detached eclipsing binaries and 13 classical variables.
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