Let T be an integral domain, M a nonzero maximal ideal of T, K = T/M,

: T \longrightarrow K the canonical map, D a proper subring of K, and R =

(D) the pullback domain. Assume that for each

, there is a

such that u is a unit in T and

, . In this paper, we show that R is a weakly Krull domain (resp., GWFD, AWFD, WFD) if and only if htM = 1, D is a field, and T is a weakly Krull domain (resp., GWFD, AWFD, WFD).