Aleatory variability in ground‐motion prediction, represented by the standard deviation (sigma) of a ground‐motion prediction equation, exerts a very strong influence on the results of probabilistic seismic‐hazard analysis (PSHA). This is especially so at the low annual exceedance frequencies considered for nuclear facilities; in these cases, even small reductions in sigma can have a marked effect on the hazard estimates. Proper separation and quantification of aleatory variability and epistemic uncertainty can lead to defensible reductions in sigma. One such approach is the single‐station sigma concept, which removes that part of sigma corresponding to repeatable site‐specific effects. However, the site‐to‐site component must then be constrained by site‐specific measurements or else modeled as epistemic uncertainty and incorporated into the modeling of site effects. The practical application of the single‐station sigma concept, including the characterization of the dynamic properties of the site and the incorporation of site‐response effects into the hazard calculations, is illustrated for a PSHA conducted at a rock site under consideration for the potential construction of a nuclear power plant.