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Rep. Rob Bishop grabbed a seventh term, Rep. Jason Chaffetz a fourth and Rep. Chris Stewart a second.

The three House incumbents, all in safe Republican congressional districts, cruised to victories Tuesday over their Democratic challengers, according to unofficial returns.

The Utah congressmen rode a national, conservative wave that is likely to give their caucus an even larger majority in the House, and, for two of them, possibly chairmanships of powerful committees.

1st District

For Bishop, a former Utah House speaker from Brigham City, his re-election likely means he will take the reins of the House Natural Resources Committee in January, a promotion that would give him oversight of public-lands agencies and more power to push through his own legislation.

Bishop beat back a second challenge by Donna McAleer, who had lost to the Republican by some 46 percentage points in 2012 in the heavily GOP district.

This time around she fared better, receving 31,668 votes to Bishop's 70,240 or 29 percent to 64 percent.

A former West Point graduate and Army officer, McAleer had charged that Bishop was a "guardian of gridlock" and tied him to the October 2013 government shutdown. Bishop countered that his likely spot over the Natural Resources Committee would allow him greater sway over the management of Utah's federal lands, which cover nearly 70 percent of the state.

"If the polls are accurate, what it's basically saying is that I'm in the position that I can do the most amount of good for the people of the 1st District," Bishop said Tuesday evening.

McAleer conceded shortly before 11 p.m., calling Bishop to say that she hopes "he's able in this new Congress to move this country forward and find some common ground."

Does she think he'll do that? "Not at all," she responded in a phone interview.

2nd District

State Sen. Luz Robles' campaign was interrupted Oct. 26, when she gave birth to her second daughter, Sol, but the candidate jumped back into the ring and even took the early-arriving baby to vote early.

"We're just happy, thrilled," Robles said earlier Tuesday. "She desired to make an entrance prior to November, so we're excited about it."

In the end, though, Robles couldn't muster nearly enough votes — 42,356 to 76,966 or 33 percent to 60 percent — to topple Stewart, who is finishing up his freshman term.

"We had set a priority of increasing participation," Robles said, "and we did."

In his campaign, Stewart, a best-selling author, touted his spot on the House Appropriations Committee, a rarity for a newcomer and a role he hopes to use to pare government spending.

"We've worked hard and I don't think we're terribly surprised," Stewart said of his victory. "But I think it's good to have another indicator that the work is paying off."

3rd District

Chaffetz glided to a fourth term. His Democratic rival, Brian Wonnacott, didn't really campaign. No yard signs. No calls. He even returned donations.

That left Chaffetz essentially unopposed. Unofficial final results showed he received 94,571 votes to Wonnacott's 29,575 or 72 percent to 23 percent.

While Chaffetz hasn't had to campaign hard against his opponent, he has been hitting the stump trying for another prize: to head the House Oversight and Government Reform Committee. Chaffetz appeared widely on TV during the recent Secret Service scandal and has hit the road to help other candidates. He even took two days to tour the U.S.-Mexico border with the Border Patrol.

Annie Knox contributed to this report.