We carefully analyze the N = 2 dual pair of string theories in four di
mensions introduced by Ferrara, Harvey, Strominger and Vafa. The analy
sis shows that a second discrete degree of freedom must be switched on
in addition to the known ''Wilson line'' to achieve a non-perturbativ
ely consistent theory. We also identify the phase transition this mode
l undergoes into another dual pair via a process analogous to a conifo
ld transition. This provides the first known example of a phase transi
tion which is understood from both the type II and the heterotic strin
g picture.