In this study, we present an inelastic demand spectrum for the design of seismically-isolated structures using lead-rubber bearings or other types of isolators with bi-linear hysteresis loops and the inelastic spectrum can be used in the design of seismically-isolated structures in a very similar manner to capacity spectrum method. The inelastic demand spectrum is a very useful design tool for visual selection of optimal isolation parameters, and eliminates the use of equivalent linear-elastic substitute structures as the displacement demand is obtained from nonlinear time history analysis. The responses of seismically-isolated structures subjected to near-source ground motions with either large forward-directivity pulses or fault-fling pulses are presented. Our analyses suggest that seismic isolation can be used to protect structures subjected to recorded ground motions currently available to us, with acceptable levels of base shear coefficient and isolator displacement, except for one component of the TCU068 record from the 1999 Chichi, Taiwan, earthquake (which contained a large permanent displacement of nearly 10 m).