The discussion comes after a man last month fired several shots on the steps of the towering Capitol in Austin.

State troopers tackled him and no one was wounded, but the incident spotlighted a predicament for lawmakers in a state where carrying handguns is not only legal but largely cherished.

Lawmakers, some of whom regularly show up armed to the job, have to sort through an array of safety options. They range from prohibiting guns in the Capitol, making everyone who steps into the building go through a metal detector, to exempting those who have a license to carry a concealed weapon. Or lawmakers could stick with current safety procedures, which permit unfettered access to all areas of the Capitol when the legislature isn't in session, effectively allowing access to people carrying guns.

Gov. Rick Perry, a concealed-weapon licensee himself who was endorsed by the National Rifle Association in his bid for re-election, is of the view that lawful gun-carrying Texans deter criminals from drawing their weapons for fear of being outnumbered. "The last thing I want is for the Texas Capitol to turn into DFW Airport," he said at a recent news conference.

But others question whether civilians' right to carry firearms should extend to the seat of state government, which is visited daily by thousands of tourists and citizens with legislative business, some of whom who aren't always happy about lawmakers' decisions.

State Rep. Eddie Rodriguez, a Democrat from Austin, favors banning the guns at the Capitol. "If you ask me point blank, I'll have to say we should not compromise on this issue," he said.

The Texas Capitol, a pinkish-granite domed behemoth in downtown Austin, houses the offices of state legislators and the chambers where they make laws.When construction of the Capitol was finished in 1888, those who entered were subject to a law dating from the turbulent post Civil-War era that banned from practically all pubic establishments an assortment of weapons, including guns, sword-canes, spears, brass-knuckles, bowieknives "or any other kind of a knife manufactured and sold for the purpose of offense and defense."

But in 1995, then-Gov. George W. Bush signed a bill that allowed anyone who was cleared by a background check and took a course, among other requirements, to carry a concealed weapon in a variety of places, including the Capitol. More recently however, a rule was put in place that requires visitors who want to witness lawmakers in action from the galleries to go through a metal detector.

The Texas Rangers, a division of the state police force, are investigating the incident, but a spokeswoman said Mr. Cardenas isn't among the 381,000 Texans who hold a concealed-carry license.

Reaction was prompt—and divided. Mr. Patrick suggested installing metal detectors, but allowing lawful gun-carriers such as him to skirt them by showing their license. Another idea: the state could let frequent visitors such as legislators, state employees and the media bypass the detectors.

"Some people outside of Texas may have this view that we're a gun-toting society; we're not," said Mr. Patrick, who believes licensees provide an added layer of security due to their training. "We're a state that has responsible gun owners."

Mr. Rodriguez believes security should be left to police. Armed volunteers could do more harm than help by confusing security officers if they pull out a weapon to defuse a dangerous situation, he said. "Who's going to know who's the good guy and who's the bad guy?"

Neither Mr. Patrick, nor Mr. Rodriguez is part of a task force that is studying several options to improve security, but they have sent in their suggestions.

Tommy Williams, a Republican senator from The Woodlands who is part of the task force, said he expected state officials to make a decision in coming weeks, but declined to reveal details about the potential measures. He said the focus is keeping people safe without restricting their access to the Capitol