"He's been good and he's handled the pressure pretty good," Gibson said of Ziegler.
Since taking over the closer's role from Bell, who took it from Putz when Putz went on the disabled list, Ziegler is 5-for-5 in save opportunities and has allowed just one unearned run in his seven appearances.
Bell, meanwhile, blew his fifth save chance on July 10, and was removed from the closer's role. Since then, he has pitched nine innings over nine appearances and allowed five hits and no walks while striking out 12.
Putz did not immediately regain his closer's role when he came off the DL on June 29, because the team did not feel he had fully regained his arm speed.
Since that time, though, it has improved.
"The ball is coming out of his hand way better, definitely," Gibson said. "Split isn't real good right now, but his slider is. Good [velocity], and he's got a lot more life on his ball right now."
Gibson has long liked Ziegler more in a setup role because he is such a ground-ball pitcher that he is valuable coming into a game with runners on base and getting hitters to ground into double plays.
For now, though, it sounds like the manager is not prepared to disrupt a good thing.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.