Although it has been established that there is a strong relationship between observed substorms and the southward component of the interplanetary field Bz, there remains a controversy concerning models explaining this relationship. An analysis of a statistical study of isolated substorms and the related interplanetary fields had previously resulted in a set of five models, and one of which would explain the data. Tests had been suggested that could eliminate some of the models but which first required that a new statistical study of substorms be undertaken. Recently, the average characteristics of such a new set of substorms and of the associated Bz have become available. The behavior of Bz in that study is strikingly different from that reported in the earlier study. This permits stringent tests of substorm models to be made. Here I report that the new data conclusively rule out three of five models consistent with the earlier study, and although further testing is required, the present data do not support the 'occurrence threshold' model described earlier. The 'appearance threshold' model, in which there typically is a 40-min lag between the time at which the interplanetary field attains its threshold value and the time at which a substorm onset is observed, is consistent with both sets of data.