Since the discovery of the transiting super-Earth CoRoT-7b, several investigations have yielded different results for the number and masses of planets present in the system, mainly owing to the star's high level of activity. We re-observed CoRoT-7 in 2012 January with both HARPS and CoRoT, so that we now have the benefit of simultaneous radial-velocity and photometric data. This allows us to use the off-transit variations in the star's light curve to estimate the radial-velocity variations induced by the suppression of convective blueshift and the flux blocked by starspots. To account for activity-related effects in the radial velocities which do not have a photometric signature, we also include an additional activity term in the radial-velocity model, which we treat as a Gaussian process with the same covariance properties (and hence the same frequency structure) as the light curve. Our model was incorporated into a Monte Carlo Markov Chain in order to make a precise determination of the orbits of CoRoT-7b and CoRoT-7c. We measure the masses of planets b and c to be 4.73 ± 0.95 and 13.56 ± 1.08 M⊕, respectively. The density of CoRoT-7b is (6.61 ± 1.72)(R p /1.58 R⊕)−3 g cm−3, which is compatible with a rocky composition. We search for evidence of an additional planet d, identified by previous authors with a period close to 9 d. We are not able to confirm the existence of a planet with this orbital period, which is close to the second harmonic of the stellar rotation at ∼7.9 d. Using Bayesian model selection, we find that a model with two planets plus activity-induced variations is most favoured.