A ''conducive domain'' is a (commutative unitary integral) domain R, with quotient field F, such that for every overring T of R, \(R\subseteq T\subsetneqq F\), the conductor \((R:T)=\{x\in F;\quad xT\subseteq R\}\) is nonzero [cf. \textit{E. Bastida} and \textit{R. Gilmer}, Mich. Math. J. 20, 79- 95 (1973; Zbl 0239.13001) and \textit{D. E. Dobbs} and \textit{R. Fedder}, J. Alg. 86, 494-510 (1984; Zbl 0531.13002)]. The authors show how the pullback point of view [cf. \textit{M. Fontana}, Ann. Mat. Pura Appl., IV. Ser. 123, 331-355 (1980; Zbl 0443.13001)] can be used to give a complete description of Noetherian, Archimedean and accp conducive domains. Moreover, some necessary or sufficient criteria for conducive Mori domains are obtained.