This story was updated June 16 at 7:20 a.m.
For people in Florida, it comes as a bit of a surprise that many observers now consider Jeb Bush -- who announced his run for president Monday -- a moderate. He certainly didn't govern like one.
"He governed as a conservative and everyone in the Florida Republican Party considered him a conservative," said Darryl Paulson, a government professor at the University of South Florida.
Bush cut taxes each of the eight years he was governor, from 1999 to 2007, for a total of nearly $20 billion. He helped streamline state government, privatizing many functions and cutting the civil service payroll by 14,000 jobs.
"Every Republican candidate in Florida was seeking to brand himself as a Jeb Bush Republican," Paulson said. "That was seen as to good housekeeping seal of approval, because that meant you were a good conservative Republican."
Bush wasn't an apostate like his immediate successor Charlie Crist, who switched allegiance to the Democratic Party. But Bush is certainly not as conservative as other presidential aspirants like Gov. Scott Walker of Wisconsin or Sen. Ted Cruz of Texas, for a couple of reasons.
And it's his own positions on a couple of issues that especially leave some Republicans wary. One is his approach to immigration. He doesn't think deporting millions of immigrants is a likely endgame scenario.
Last month, Bush told a group of New Hampshire business owners that the "grown-up plan" for immigration would include not only border security but a chance for undocumented immigrants to gain legal status and perhaps citizenship. "Let's let these folks achieve earned legal status where they work, where they come out of the shadows," he said.
The other area where Bush breaks with current GOP orthodoxy is the Common Core, which he continues to support even as opposition to the education standards becomes something like a litmus test within his party.
Times have changed. On education, Bush appeared to be in the conservative forefront back when he was still in office. He injected competition into public schooling via charter schools -- a movement he had helped pioneer -- private school vouchers and a mandatory testing regime that predated the federal No Child Left Behind law (and which Jeb Bush always insisted was superior to his brother's).
"His changes to education infrastructure and how we hold our educational system accountable has to be near the top of the list of his accomplishments," said Pete Dunbar, a Tallahassee lobbyist who served as a top aide to Gov. Bob Martinez while Bush was commerce secretary.
Bush benefited from changes to Florida's state government structure, while prompting some others. The post of Florida governor had historically been relatively weak, but voters approved a constitutional amendment in 1998 that cut the cabinet in half, from six elected members to three, putting more power directly in the governor's hands.
And term limits began having a strong effect on the legislature during Bush's tenure, weakening what had been a stronger counterweight to the governor.
Bush was the first GOP governor to work with a Republican-dominated legislature in the state since 1874 and he convinced both legislators and voters to give his office more authority -- notably, the power to appoint judges, which previously had been shared with the state bar association and voters.
"He's not afraid to challenge the status quo," said GOP state Rep. Dennis Baxley.
"He would ask what I call the Jeb Bush question -- if we weren't already doing it this way, how would we do it?" Baxley said. "It's a good question. It strikes fear in some, but it was refreshing."
Bush abolished affirmative action in university admissions and state contracting by executive order, triggering protests, and also signed the "stand your ground" self-defense law that drew criticism after the killing of Trayvon Martin.
As the release of his gubernatorial emails has shown, Bush never seemed to stop working or to overlook government problems big or small. He used his line-item veto authority to block more than $1.5 billion worth of earmarks in all.
He wooed companies to Florida, many of which he helped bring along through aggressive use of tax incentives and other state dollars, notably in the biotech sector.
Unemployment was just 3 percent in Florida when he left office. The state consistently led the nation in job growth his last couple of years in office, despite a string of devastating hurricanes.
Bush received praise for his handling of natural disasters. A new book about his tenure is called Conservative Hurricane: How Jeb Bush Remade Florida.
"This office has more authority to create the agenda and implement it," Bush said as he was leaving office. "My gift is that we've shown that governors can be activists, they can be reformers, if they want to."
Stepping down ahead of the recession, Bush also managed to leave the state with a $3 billion surplus.
His tenure certainly wasn't perfect. His privatization push led to scandals and complaints about sweetheart deals. Human service functions -- particularly child welfare -- suffered from budget cuts and mismanagement. The Department of Children and Families managed to lose track of some 500 children under state care.
Still, Bush was pretty popular as he left office. A Quinnipiac University poll conducted as Bush was preparing to leave office in 2006 showed 55 percent of Floridians approved of the job he was doing, compared with 36 percent who disapproved.
"You seldom find a governor who actually does something and is a transformative governor, and yet has such high approval ratings," Paulson said.
Dunbar credits Bush with leaving the state in good shape and better prepared than it might otherwise have been for continuing population growth that has since made Florida the third most populous state.
Bush may or may not be the exact perfect fit for his party in 2016, but there's little doubt he was a successful and powerful governor.
"In my opinion, Jeb Bush was one of, if not the most, effective governors we've had," Dunbar said.