Abstract |A comparative study of alternative Intensity Measures (IMs) for structures of rocking response is presented, focusing on the salient characteristics that define the selection of an optimal IM for the problem at hand. An IM may play the role of an interfacing variable, linking hazard with fragility/vulnerability for the risk assessment of structures, or it may only be employed as a proxy for predicting structural response under a given ground motion. In the first case, low conditional variability (high efficiency) and low conditional dependence on seismological parameters (high sufficiency) are needed. For response proxy usage, one may place more importance on the predictive capability of the IM within a simple regression model, favoring high correlation and low fitting errors over an extended range of response. The results showcased that (i) the peak ground acceleration and peak ground velocity, tend to be highly efficient and sufficient in specific regions of rocking response, that is, onset of rocking and overturning, respectively, but not necessarily everywhere; (ii) the average spectral acceleration shows a more consistent performance at the cost of requiring the definition of a proper period range; (iii) magnitude sufficiency is generally more difficult to achieve, compared to the distance from the rupture, and (iv) IMs that may be unsuitable for risk and vulnerability assessment, can still be highly effective as response predictors in statistical models.