A probabilistic seismic hazard analysis performed for rock conditions and modified for soil conditions using deterministic site amplification factors does not account for uncertainty in site effects, which can be significant. One approach to account for such uncertainty is to compute a weighted average amplification curve using a logic tree that accounts for several possible scenarios with assigned weights corresponding to their relative likelihood or confidence. However, this approach can lead to statistical smoothing of the amplification curve and possibly to decreased computed hazard as epistemic uncertainty increases. This is against the expected trend that higher uncertainty leads to higher computed hazard, thus reducing the incentive for practitioners to characterize soil properties at a site. This study proposes a modified approach in which the epistemic uncertainty is captured in a plot of amplification factors versus period. Using a case history, the proposed method is shown to improve the issue with the weighted average method for at least two oscillator periods and to yield similar results for two other periods in which the highlighted issue is less significant.