Predictors of seismic structural demands (such as inter-storey drift angles) that are less time-consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square-root-of-sum-of-squares (SRSS) rule by taking a first-mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post-elastic first-mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single-degree-of-freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third-mode response for long-period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright ?? 2006 John Wiley & Sons, Ltd.