The 19th-ranked Lobos, though, realize they're in for a tough test against UAB and its own standout big man, C.J. Washington.
New Mexico faces the unbeaten Blazers on Thursday in a first-round matchup featuring two of the top rebounding teams in the country.
The 6-foot-9 Bairstow finished with 22 points and 11 rebounds in an 88-52 win over Alabama A&M on Nov. 9, with the 7-foot Kirk adding 16 points and 12 boards.
Each then went 9 for 13 from the field as Bairstow scored a career-high 29 points while Kirk finished with 24 and 13 rebounds in Sunday's 109-93 win over Charleston Southern.
The pair has combined for 46.2 percent of the team's scoring and 47.7 percent of its rebounds.
''I'm really proud of the way Bairstow and Kirk have played,'' coach Craig Neal said.
Though New Mexico has cruised to a solid start, guard Kendall Williams knows it still has plenty to prove, beginning with winning a tournament that doesn't feature another ranked team.
"It's our first chance to win a championship," Williams, who had 20 points and 10 assists in the last game, told the team's official website. "That's what we pride ourselves on, so we are going to go down to Charleston and try to win a championship.
"Now, we get thrown into the fire."
Getting through UAB (3-0) likely won't be easy. The 6-8 Washington has been stellar in his first season after transferring from junior college, averaging 20.0 points and 8.3 rebounds while shooting 62.5 percent.
He went 11 of 14 from the field and finished with 25 points and 10 rebounds in last Thursday's 81-69 win over Troy. The Blazers won the battle on the boards 53-24, and they rank second in the nation with a plus-20.7 rebounding margin.
New Mexico is fourth at plus-18.5.
"They have size. They are a great offensive rebounding team," Neal said. "We have to guard. We're going to have to get back to work because we're not going to be able to win games allowing people to score easily."
UAB has spread around its scoring, with guard Chad Frazier (12.0 points per game), forward Rod Tucker (11.7) and center Fahro Alihodzic (10.7) also averaging in double figures.
"It's real helpful because they can't have a scouting report to stop this person or that person," Washington told the team's official website. "We have five people that's starting who can score and people coming off the bench that can get buckets for us as well."
Robert Williams is averaging 9.0 points and 6.3 rebounds as a reserve after starting 32 of 33 games last season.
"He's unbelievable," coach Jerod Haase said. "He's the team captain. After one of our (exhibition) games, he didn't play a ton and came up to me and said 'Coach, whatever you need me to do, I'm all in.' Right now he's playing great."
UAB has lost six straight against ranked opponents since beating No. 20 Butler on Dec. 22, 2009.
The winner of this matchup - the first between the schools - advances to Friday's semifinals to face Nebraska or Massachusetts. The losers meet the same day in the consolation bracket.
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