Under-coverage and nonresponse problems are jointly present in most socio-economic surveys. The purpose of this paper is to propose an estimation strategy that accounts for both problems by performing a two-step calibration. The first calibration exploits a set of auxiliary variables only available for the units in the sampled population to account for nonresponse. The second calibration exploits a different set of auxiliary variables available for the whole population, to account for under-coverage. The two calibrations are then unified in a double-calibration estimator. Mean and variance of the estimator are derived up to the first order of approximation. Conditions ensuring approximate unbiasedness are derived and discussed. The strategy is empirically checked by a simulation study performed on a set of artificial populations. A case study is derived from the European Union Statistics on Income and Living Conditions survey data. The strategy proposed is flexible and suitable in most situations in which both under-coverage and nonresponse are present.