The historical tsunami that occurred on July 30, 1627 in Gargano (Apulia, Southern Italy) was generated by a very large earthquake (I=XI MCS scale) that produced severe damage in the whole promontory. In spite of the large number of macroseismic observations, it is not possible to determine the epicenter and the generative fault position unambiguously. Though the historical sources concerning the tsunami are not extremely detailed, yet they allow us to locate and to evaluate the most important wave effects on the coasts. A prior tsunami study, conducted by performing numerical simulations based on integrating shallow-water equations via a finite-element technique, assumed a genetic dip-slip focal mechanism on faults that were temptingly placed in different positions both on land and offshore (Tinti and Piatanesi, 1996). The present work, which represents a natural continuation of that investigation, aims mostly at constraining the location of the tsunamigenic fault on physical grounds; this is accomplished by means of tsunami simulations on a new finer finite-element grid and by using the earthquake sources described in the previous paper as well as new inland faults striking N-S. It is shown that mesh refinement leads to better solutions, especially as far as the computation of the maximum elevation along the coast is concerned. Determining the position of the causative fault was one of the main motivations of this research. It has been found that compatibility with the available tsunami data requires that the fault be located inland in the coastal area embracing the Lesina Lake and the mouth of the Fortore River: the strike, however, is not too well constrained, though E-W striking seems preferable to N-S.