To a designer of a nonlinear structure, there is nothing more attractive than a real or fictitious ground motion time history whose response spectrum matches the target design spectrum. Frequency-domain scaled, design spectrum compatible time histories (DSCTH) are widely used in analysis and design of special structures, particularly seismic-isolated buildings. Their use has been even mandated by some code provisions. At the first glance, it seems that DSCTH records furnish designers of earthquake resistant structures with a consistency and compatibility bridge between the two very different worlds of elastic and inelastic response. Closer examination, as presented in this paper, reveal however that there are significant potential problems associated with uncontrolled use of DSCTH records in seismic design. It is shown that the use of design spectrum compatible time histories can lead to exaggeration of displacement demand and energy input. This in turn can distort the expected performance of the structure when subjected to design earthquake ground motions.