Among various trial models ofP-wave travel times, there exists at least one model which best predicts the times of first arrivals from a certain region at a set of recording stations even if no attempt is made to correct the travel-time standards against known station errors and source bias. In teleseismic distance range (25°≦Δ≦100°) and surface-focus case, the possibility of statistically establishing which of the twoP models, viz. Jeffreys-Bullen and Herrin, is more appropriate for each of the four source regions, viz. Southern Nevada, Aleutian Islands, Eastern Kazakh and Novaya Zemlya, is discussed in this paper. Data corresponding to a set of underground explosions from these regions form the basis of such an analysis. The Herrin model is found to be better applied to Aleutian Islands region while the Jeffreys-Bullen model seems more appropriate for each of the remaining three regions.