A high-frequency approximation for nongeometrical arrivals due to highly concentrated sources adjacent to the interfaces between two different elastic media has been developed following their detection in the real field data by Gutowski et al. (1982). In our approach, the “★” waves are associated with secondary saddle-point contributions of the contour of integration circumventing branch points in the integral representation of transmitted wave field. Our formulas are presented in a simple form suitable for an easy incorporation into any ray synthetic seismogram computation. The range of validity of our approximations is discussed and their accuracy tested by comparing the pertinent ray seismograms with their equivalents produced by the Alekseev-Mikhailenko method. A good match between both sets of seismograms suggests that our high-frequency approximations for “★” waves are well justified as are our formulas derived for the head wave-like arrivals driven by the “★” waves, and seen in the full wave field seismograms and detected in real data as well.