Modern ground-motion prediction models use datasets of recorded ground-motion parameters at multiple stations during different earthquakes and in various source regions to generate equations that are later used to predict site-specific ground motions. These models describe the distribution of ground motion in terms of a median and a logarithmic standard deviation ( e.g. , Strasser et al. 2009). This standard deviation, generally referred to as sigma (σ), exerts a very strong influence on the results of probabilistic seismic hazard analysis (PSHA) ( e.g. , Bommer and Abrahamson 2006). Although there are numerous examples of sigma being neglected in seismic hazard, it is now generally accepted that integration over the full distribution of ground motions is an indispensable element of PSHA (Bommer and Abrahamson 2006). Attempts to justify, on a statistical basis, a truncation of the ground-motion distribution at a specified number of standard deviations above the median have proven unfeasible with current strong-motion datasets (Strasser et al. 2008). The most promising approach to reduce the overall impact of sigma on the results of PSHA is to find legitimate approaches to reduce the value of the standard deviation associated with ground-motion prediction equations (GMPEs). The present state-of-the-practice of seismic hazard studies applies the standard deviations from ground-motion models developed using a broad range of earthquakes, sites, and regions to analyze the hazard at a single site from a single small source region. Such practice assumes that the variability in ground motion at a single site-source combination is the same as the variability in ground motion observed in a more global dataset and is referred to as the ergodic assumption (Anderson and Brune 1999). In recent years, the availability of well recorded ground motions at single sites from multiple occurrences of earthquakes in the same regions allowed researchers to estimate the ground-motion variability …