Near-source ground-motion records affected by directivity may show unusual features in the signal resulting in low-frequency cycle pulses in the velocity time history, especially in the fault-normal component. Such an effect causes the seismic demand for structures to deviate from that of so-called ordinary records. This circumstance may be particularly hazardous for structural engineering applications if it is not properly accounted for. In fact, current attenuation laws are not able to capture such effects well, if at all, and therefore current probabilistic seismic hazard analysis (PSHA) is not able to predict this peculiar spectral shape. This failure may possibly lead to an underestimation of, in particular, the nonlinear demand. Accounting for pulse-type records in earthquake engineering practice should be reflected both in the PSHA and in the record selection for seismic assessment of structures. These applications require a model for the probability of occurrence of pulselike records. Herein such a model is proposed on an empirical basis. A set of pulselike fault-normal ground motions from the Next Generation Attenuation of Ground Motions (NGA) Project dataset, as systematically identified by Baker (2007), is used. The independent variables studied are chosen from those considered by seismologists to affect the amplitude of directivity pulses. Issues related to the dataset and the explanatory power of the proposed models are also discussed.