They never explained the reasons why they soured on Couture, saying what went wrong was confidential.
One bit of fallout from the regents' handling of Couture's departure will be felt Monday at the Capitol. State Rep. Jeff Steinborn said he will introduce a bill calling for three of the regents at NMSU and three at the University of New Mexico to be elected in statewide balloting instead of being appointed by the governor.
Under his bill, other regents would continue to be selected by the governor, but the field of candidates would be limited to those recommended by a newly formed higher education nominating commission. This system would be similar to the way state district judges are appointed.
The nominating commission would screen and recommend regent candidates for all seven of the state's four-year colleges and universities.
Steinborn, D-Las Cruces, said Couture's buyout was "a galvanizing event" in his push for reform. "The whole way it was handled bothered me."
But he has broader reasons for introducing his bill.
Steinborn said the existing system of appointing regents had become too politicized, as governors select donors, friends or politically connected insiders, often without regard to qualifications.
"They've kind of become the ambassadorships of New Mexico politics," he said in an interview.
His criticisms, he said, were not a swipe at Republican Gov. Susana Martinez, who is beginning her third year in office.
"This is not anti-Martinez. This is a critique of our system, which is not rigorous enough," Steinborn said.
He cited a 2008 study by a Michigan State University professor that found the top-performing states in higher education use appointment processes with requisite qualifications to decide the fitness of regent candidates. New Mexico, where the governor can pick virtually anybody she wants to serve as a university regent, ranked 49th of the 50 states in that study.
Steinborn's plan of electing a handful of regents and creating a nominating commission to help pick the rest would require approval from the Legislature and then the state's voters in November 2014. That is because the New Mexico constitution now gives the governor sole power over appointments to the governing boards of four-year colleges and universities.
Steinborn, who served two previous terms in the state House of Representatives, regained a seat in the November election. He has since been working the Capitol corridors and offices, making his pitch to fellow legislators for a revamped system of selecting university regents.
He said a hybrid of some elected and some appointed regents makes sense for UNM and New Mexico State.
His bill would expand the number of regents at New Mexico State from five to seven, the same as at UNM. Voters statewide would elect three regents at each of the universities to four-year terms.
Because New Mexico State is a land-grant university and UNM has a statewide enrollment base, an election system should be part of both boards of regents, Steinborn said.
But he decided not to seek elections of all regents at UNM and New Mexico State for a simple reason. In a statewide election, it is possible that nobody from Las Cruces would win a seat on the New Mexico State Board of Regents, leaving the university's hometown with no representative.
His bill would require that two of the appointed regents for UNM and two for New Mexico State come from the county where the main campus is located.
In addition, another regent for each university would have to come from a community that hosts a branch campus.
A student would be the seventh regent on both of the governing boards. The governor would appoint the student regents.
In Steinborn's view, elections and higher standards for appointees would create stronger governing boards and better universities.
"We get greater accountability, more public involvement, more dynamism," he said.
Martinez might disagree that the system is broken.
This month she chose former state Rep. Conrad James, a fellow Republican, to serve as a UNM regent. James, 38, lost his bid for re-election in November, but he has sterling academic credentials.
A research engineer at Sandia National Laboratories, James received a bachelor of science degree in electrical engineering from Notre Dame and a master's degree and Ph.D. in engineering physics from Cornell.
Martinez in 2011 chose retired Lt. Gen. Bradley Hosmer as a UNM regent. He was superintendent of the Air Force Academy and president of the National Defense University.
Steinborn, though, said people who become university regents under the current system tend to move in political circles. Excellent candidates may not be in that same loop, he said.
At New Mexico State, one of the regents is Javier Gonzales, chairman of the state Democratic Party. Former governor Bill Richardson appointed Gonzales as a regent in 2008 and he became Democrats' party leader the following year.
The Higher Education Nominating Commission would be for all regent appointments at New Mexico Tech, Eastern New Mexico, Western New Mexico, New Mexico Highlands and Northern New Mexico College. Another component is that the Legislature would establish minimum qualifications to serve as a regent.
Steinborn's bill also would empower the nominating commission to recommend regents for the School for the Blind, School for the Deaf and the New Mexico Military Institute. The governor now also appoints the supervising boards of those schools.