Limb darkening is an important stellar phenomenon, and must be accounted for in the study of stellar spectra, eclipsing binaries, transiting planetary systems, and microlensing events. The power-2 limb-darkening law provides a good match to the specific intensities predicted by stellar atmosphere models: better than other two-parameter laws and only surpassed by the four-parameter law. Predictions of the limb-darkening coefficients for the power-2 law are not widely available. We therefore compute them, using stellar atmosphere models generated by the ATLAS (plane-parallel) code. Limb-darkening coefficients were computed for the space missions Gaia, Kepler and TESS as well as for the photometric systems uvby, UBVRIJHK and SDSS ugriz. The calculations were performed by adopting the Levenberg-Marquardt least-squares minimization method and were computed with a resolution of 100 equally-spaced viewing angles. We used 9586 model atmospheres covering 19 metallicities, effective temperatures of 3500 to 50000K, log g values from 0.0 to 5.0, and microturbulent velocities of 0, 1, 2, 4 and 8 km/s. We confirm the superiority of the power-2 law, in terms of the quality of the fits, over other two-parameter laws. This is particularly relevant for the quadratic law, which is widely used. We recommend the use of the power-2 law in cases where a two-parameter law is needed.