The irradiance of the Sun is reconstructed from 1700 to the present, whereby the contributions of active regions and the quiet Sun are modelled separately. A method is proposed which allows the contribution of active-region faculae and sunspots to irradiance changes to be isolated even when only a single proxy of solar activity, such as sunspot relative number, R-z, is available. The resulting reconstruction explicitly takes the non-linear relationship between R-z and irradiance variations into account. Nevertheless, due to the decreasing accuracy of the solar proxy data the accuracy of the reconstruction decreases at earlier epochs. The main uncertainty, however, lies in the reconstruction of the quiet-sun irradiance variations.