A revision of Israel's extension of Vaidya's spacetime is proposed in order to apply the procedure to more general spacetimes. Israel's procedure is reformulated to obtain the extension even if the only available function is the mass in the non-extended region. The additional demands on analiticity and energy conditions are discussed. Eventually, the method is applied to the extension of Vaidya-Reissner-Nordström's spacetime. The different cases arising are described and their conformal diagrams presented.