In his two years in office, the news media has raised questions about six of his appointees.
He fired four of them last year in the wake of critical articles in the Phoenix New Times and other publications.
Two other appointees have also come under scrutiny, including State Parks Director Sue Black, who was the subject of an Arizona Republic article on Tuesday.
Here's a look at Ducey's troubled selections and the issues behind the criticism:
1. Tony Bouie, former State Lottery director
Bouie is a former Tampa Bay Buccaneer who previously never had held a job in government, and had spotty experience as a businessman. One lawmaker noted that his most recent job before his appointment was his work as a substitute teacher.
Ducey forced Bouie to resign two days after a hard-hitting article in the New Times.
Based on a tip, the article covered allegations including Bouie's use of a state car and his hiring of athlete friends to fill top positions at the agency.
The state Attorney General's Office later cleared him of any criminal wrongdoing related to the scandal.
Bouie's now battling a lawsuit by two former Lottery employees, Karen Bach and Jessica Reimann. They claim that Bouie unfairly fired them, replacing them with two male friends of Bouie's.
Court records show that a settlement attempt in the suit last month didn't work out; the parties are moving closer to a trial.
2. Dona Marie Markley, former Juvenile Corrections director
Ducey likes to put former business people in key state government positions. Markley, though, had worked for the state for more than 30 years. She'd also served as acting head of juvenile corrections for two years before Ducey made her position permanent.
She submitted an "involuntary resignation" in September 2016 following two stories in the Arizona Republic about her firing of employees with health problems. The governor later said that six people she terminated would be reinstated.
Markley claimed the firings had followed Arizona Department of Administration advice and has threatened to sue the state for $750,000.
3. Tim Jeffries, former state Department of Economic Security director
New Times explored the rise and fall of Jeffries in a cover story last week.
In his 21-month run, Jeffries reportedly improved overall employee morale and agency efficiency. But he failed the headline test. Several times.
Employees and the ex-employees began complaining to the media that Jeffries had created a culture of fear, and that many of the vanquished hadn't deserved to be fired.
Jeffries also received criticism — and, again, some praise — for his frequent religious references at work and in e-mails to the 7,600-member DES staff.
And he got in trouble for sending the staff a one-sided political message that appeared to violate state law.
Ducey demanded Jeffries' resignation after Leah Landrum Taylor, the state Senate Minority Leader and a deputy director at the DES, accused him of buying alcohol for employees in Nogales on state time.
Jeffries said he bought the alcohol after work hours and that his former spokeswoman, Tasya Peterson, was in Nogales with him and could vouch for him.
Peterson, who still works for the DES as a taxpayer-funded public information officer, refuses to say when the alcohol was served.
The former director has been on a self-promotion tour in recent weeks, giving his side of the resignation to the media. And he's secured job recommendations from Ducey and at least one state legislator.
4. David Farca, former president of the Arizona-Mexico Commission
Ducey cited Farca's "exceptional entrepreneurial experience" in a news release announcing Farca's appointment in 2015.
Local businessman Greg Hoyt sued Farca and his company in late 2015 over a soured deal to renovate Hoyt's vacation home in Cabo San Lucas. He alleged consumer fraud, breach of contract, unjust enrichment, and breach of good faith and fair dealing.
Worse, the Internal Revenue Service had filed five federal liens against Farca for unpaid tax bills of tens of thousands of dollars. The first lien was in 2013, meaning that whoever vetted Farca for Ducey should have seen it.
The Arizona United Soccer Club fired Farca as its president a few weeks after a New Times' article about the lawsuit and his money problems.
Ducey then asked for Farca's resignation in December.
5. Sue Black, Arizona Parks Director
Former Wisconsin Governor Scott Walker recommended Black to Ducey for the parks director job, possibly as a political favor.
She came with impressive credentials and a record of apparent success, as New Times reported in 2015.
But she'd also been fired in 2012 as head of the Milwaukee County Parks Department — she claimed it was for political reasons.
Walker sent a congratulatory tweet in 2013 about Black's purchase of the Milwaukee Wave soccer team. But the deal turned bad for Black — she got sued after failing to make payments on the $100,000 loan she took out to buy the team.
Black was the subject of a legal claim against the state in April 2016, Craig Harris of the Arizona Republic reported on Tuesday.
Lawyer Emily Jurmu, who had worked under Black, alleged in the claim that Black "berated employees, disclosed confidential information, used racial slurs, got drunk and belligerent while representing the agency at conferences, and unsuccessfully pressured an employee to violate the state procurement code."
Jurmu had a six-month deadline to file a lawsuit after making the claim, but never did.
However, Harris reported that the claim sparked a state investigation against Black that's still ongoing.
6. Debbie Moak, director of Governor's Office of Youth, Faith and Family
A New Times article in December detailed how Moak used state e-mail, work time, and her staff's time to help defeat Prop 205, the marijuana-legalization initiative that state voters rejected in November.
State law bans the use of any "valuable" state resources, including employees' time, to push a political message.
Moak denies the claim, saying that she used personal or vacation time for work she did on the opposition campaign during work hours. However, it's unclear if she documented that time — the governor's office has yet to release her log of personal time or vacation time for 2016.
Her boss, Ducey, was an unofficial volunteer for the opposition campaign, Arizonans for Responsible Drug Policy, helping raise millions for the group.
At the same time, Moak was a key resource for ARDP's campaign. E-mail records show she worked closely with former ARDP chair Seth Leibsohn and Axiom Public Affairs, a firm run by Ducey insiders including Sean Noble.
Some of Moak's e-mails showed that Moak's assistant, Deborrah Miller, had been communicating with Leibsohn and Axiom members on behalf of Moak.
Ducey's office is still working on a December request by New Times for Miller's e-mails with Leibsohn and Axiom employees.
It's anyone's guess what Ducey will do with Black or Moak.
Although the governor takes chances with some of the people he appoints, recent history also shows he'll give them the boot if necessary.