In order to estimate the inelastic seismic response of structures modern design codes such as the ASCE7 or Eurocode 8 allow for the use of a family of scaled natural accelerograms in conjunction with nonlinear time-history analysis. In view of this, a number of selection and scaling criteria have been proposed over the years. When it comes to scaling, the traditional approach has been to think in terms of scaling the amplitude of the accelerograms to match the intensity of the seismic input to that associated with the design spectrum. Less attention has been devoted to dual scaling (i.e. a combination of time and amplitude scaling). When it comes to the intensity to match, it is now clear that the matching of spectral acceleration does not appear to be the one and only best option for all possible combinations of the fundamental seismic parameters of the structure under analysis, i.e. fundamental period and inelastic strength. This work presents a comparative study where ductility demands of inelastic structures are estimated by time-history analysis using families of natural accelerograms scaled by different approaches. The first type of scaling criteria deals with amplitude scaling guided by either spectral acceleration or spectrum intensity; therefore no modification of the frequency content of the seismic input is imposed. The second type of scaling criteria includes methods relying on dual scaling with the view of minimising the geometrical differences between the response and the design spectra with the option of accounting for the period and strength of the structure under analysis. It is concluded that dual scaling offers an interesting and yet simple approach to make an effective and more flexible use of natural accelerograms in engineering practice