Cook, R-Ruidoso, introduced legislation two years ago that would have allowed people with permits for concealed handguns to bring their firearms to public schools, college campuses, liquor establishments, state parks and onto buses.
Gov. Susana Martinez, also a Republican, disagreed with his bill, notably the section for guns in schools. His measure died a quick death in a committee.
Now Cook has introduced a streamlined bill that would allow concealed firearms in licensed liquor establishments, including restaurants.
Cook said in an interview that his constituents want the gun-rights law expanded for safety reasons. He said they are most vulnerable to an accident when disarming themselves or holstering a handgun. Having to remove a gun before going to dinner at a restaurant heightens the safety problem, Cook said.
In addition, those with carry permits do not like leaving their guns in cars when they enter a liquor establishment. That creates the possibility of theft, Cook said.
His proposal still would allow restaurant and bar owners to ban concealed firearms by posting signs in "a conspicuous location of each public entrance." Owners or managers also could enforce a ban by verbal instruction to patrons.
Cook said that, given the amount of government regulation businesses face, adding signs would not be a burden.
Another issue will be whether the Legislature, controlled by Democrats, is in the mood for even a modest expansion of gun laws after mass shootings last year in Newtown, Conn., and Aurora, Colo.
"I'm not completely tone deaf. I know the recent tragedies have heightened sensitivities, but I hope we can have a rational conversation about this," Cook said.
His proposal is House Bill 137. It may have a better chance than a gun bill by Rep. Miguel Garcia, D-Albuquerque.
Garcia's proposal would require background checks of people who buy firearms in private transactions and at gun shows. The state Department of Public Safety would be responsible for doing the background investigations.
The agency would have to set up a seven-day-a-week hotline and perhaps add an employee to man it.
Garcia outlined his proposal in early January and introduced it this week. It is House Bill 77.