A well‐known difficulty in the popular simulations of earthquake ground motions for seismic hazard assessment using the point‐source model is overprediction of high‐frequency spectra. Ad hoc high‐cut filtering, known as or the kappa effect, is required to render the high‐frequency content to match observations. The physical origin of such filtering’s realistically occurring in nature has remained largely unclear. The difficulty is naturally resolved if (1) the shape of the source time function is allowed to deviate from the traditional form radiating the omega‐square spectrum and replaced by the function producing the high‐frequency falloff not equal to the power of 2, and (2) the high‐frequency suppression due to finite‐fault dimensions (the finite‐fault directivity) is accounted for. The verification database consists of 20 earthquakes in the magnitude range from 4 to 6 recorded in boreholes on rock sites in southwestern Japan by the KiK‐net network. The events are those observed by the greatest number of stations. Path‐effect corrections using three independently determined attenuation laws lead to the isolation of the average observed source spectra. Simulations of the spectra through the kappa‐filtered omega‐square model offer no advantage over those using the omega‐n source model combined with the finite‐fault effect. The inclusion of fault directivity thus eliminates the need for kappa filtering. The high‐frequency suppression, required to simulate realistic ground‐motion spectra, can be fully explained by the source effect with clear physical meaning.