t-invertibility and Bazzoni-like statements

We show that if D is an integral domain such that every nonzero locally principal ideal of D is invertible then every invertible integral ideal of D is contained in at most a finite number of mutually comaximal invertible ideals. We use this result to provide a direct verification of Bazzoni's conjecture: A Prüfer domain D such that every nonzero locally principal ideal of D is invertible is of finite character. We also discuss some, star-operation-theoretic, variants of the abovementioned conjecture.