PRESIDENT OBAMA’S sweeping proposals to combat gun violence represent a sound response to the mass shootings that have horrified the country. In his legislative proposals and executive actions announced Wednesday, the president and Vice President Biden showed a willingness to confront a difficult problem head-on — a problem that is not only about laws but also about culture and mental-health care.

The trouble with the package is that, in its totality, it is probably politically unrealistic. Powerful lobbies, beginning with the National Rifle Association, will fight every legislative provision; some of these provisions, like a proposed ban on assault weapons, appear to have poor odds of passage by this Congress. Supporters of tighter regulation will have to choose their battles. So it seems important to single out from Mr. Obama’s list what is most important — and most politically possible.

By those standards, our highest priority would go to improving the background-check system for gun purchases, for which there is strong public support. Some of this can be done by executive order: Mr. Obama vowed to beef up the National Instant Criminal Background Check System. Four of Mr. Obama’s 23 executive actions Wednesday involve improvements to the database, overcoming the reluctance of states to share records and ensuring that federal records are also reported.

At the same time, the president said he would ask Congress to require checks for all gun sales, closing a loophole that permits 40 percent or more of private gun transactions to be made without review. This vital measure should be able to win bipartisan support; it will not threaten the rights of any legitimate gun purchaser or owner.

Another high priority is Mr. Obama’s request that Congress ban the sale of high-capacity ammunition clips. In a semiautomatic weapon, each pull of the trigger not only fires a bullet but also pulls another into the chamber. When magazines grow larger, so does the potential death toll. The president proposes to limit all magazines to 10 rounds, compared with the 30-round magazines and larger used in recent atrocities. As with the gun-show loophole, polls show that most Americans favor the limit of magazines; it’s reasonable to expect that Congress would, too.

A third needed measure would close a loophole that allows “straw buyers” to receive only a slap on the wrist for passing a gun to a criminal or trafficker. In addition to making it easier for American criminals to acquire guns, straw purchases have been central to the trafficking of U.S. guns to Mexico, where they have fueled an epidemic of drug-related murders.

Finally, Mr. Obama is seeking to strengthen the Bureau of Alcohol, Tobacco, Firearms and Explosives, a division of the Justice Department that has been without a permanent director for six years — and lacks sufficient muscle to stand up to the gun lobby. He promised to nominate B. Todd Jones, the interim acting director; Congress, which stalled Mr. Obama’s previous nominee under pressure from the gun lobby, ought to go along.

The political battle over better gun regulation has just begun, and no one questions that it will be long and difficult. The White House has faced squarely the need for a serious agenda; now it must press hard to pass those measures that can attract broad congressional support.