This study presents an alternate site‐response model to the existing ground‐motion prediction equation (GMPE) from our previous study with some calibration to the magnitude term. We used a new site‐response proxy that combines (the travel‐time‐averaged shear‐wave velocity to 30 m depth) with the engineering bedrock depth . is available for many strong‐motion recording stations. However, GMPEs using do not directly account for the response of the soil layers between 30 m and bedrock depth. Site period (four times the shear‐wave travel time to the engineering bedrock depth) has also been used in recent GMPEs, with being considered a theoretically better parameter than a pseudosite period (four times the shear‐wave travel time to a depth of 30 m). Obtaining the shear‐wave velocity profiles between 30 m and for a deep soil site can be expensive, whereas obtaining bedrock depth based on the geotechnical description of borehole data may be relatively easy. We used velocity profiles from the Kyoshin net and Kiban–Kyoshin net strong‐motion networks and found that a pseudosite period and have an excellent correlation with a small standard deviation at all spectral periods, suggesting that is a suitable site‐effect parameter. The poor correlations between and and between and for sites with led to poor model performance at long spectral periods. We modified a GMPE by replacing with , and we made a minor modification to the moment magnitude term of the GMPE that was necessary for the new site term. The response spectra predicted by models using , , and at short spectral periods up to 0.6 s are generally similar. At long spectral periods, the spectra predicted by the are much smaller than those from the other two GMPEs. For all spectral periods, is an excellent substitute for .