A D.C. Council committee agreed Wednesday to roll back some city rules for possessing a firearm in the District, including eliminating a vision test, a five-hour training course, ballistics testing and a ban on some types of ammunition.

But the bill, which comes as the city is still assimilating the 2008 Supreme Court decision that struck down a ban on owning a handgun, faces an uncertain future when it comes up for debate before the full council this month.

Council member Phil Mendelson (D-At Large), chairman of the Judiciary Committee, pushed the bill through his committee Wednesday to try to reform city gun laws that are widely viewed as the toughest in the nation.

The new rules are designed to insulate the city from lawsuits while streamlining rules that require residents who wish to keep a handgun at home to register their weapons with the city.

In the landmark Heller v. District of Columbia , the Supreme Court overturned the District’s three-decade-long handgun ban. The justices determined that the Second Amendment grants individuals the right to possess guns for self-defense, but that governments may impose reasonable restrictions.

After that ruling, the D.C. Council approved regulations that permit residents to register certain handguns once applicants pass a written examination and provide proof of residency and good vision. People are not allowed to carry guns outside their homes in the District.

While the number of legal gun owners in the District remains small, the city continues to face court challenges and scrutiny over its gun laws.

Earlier this year, the Washington Times published a series detailing a cumbersome set of regulations that often meant a months-long process for a resident to legally acquire a handgun in the District.

Mendelson’s bill does not change registration requirements, nor does it roll back laws stating that residents can register only one handgun per month.

But the bill would eliminate the required vision test for applicants — although applicants will still have to provide documentation that they are not legally blind.

Mendelson is also proposing to scrap requirements that applicants complete a five-hour training course, including one hour on a gun range. Instead, the city’s police chief can implement a “minimal” training requirement, such as requiring applicants to watch a safety video.

Although residents would be required to register their weapons with police, they would no longer have to submit their guns to police for ballistic identification before taking them home, according to the legislation.

Under the current law, gun owners are required to submit to a background check every six years. The proposed bill removes that provision; residents, however, would still need to renew their registration by mail, online or in person.

Addressing strict city laws banning possession of ammunition, the bill clarifies that individuals with a legally registered gun can possess ammunition, even if it is “a caliber different from the firearm they registered,” according to a council summary of the bill.

But the bill increases penalties for violating a city ban on “cop-killer bullets,” according to a letter Mendelson sent to his colleagues. Such ammunition is capable of piercing the ballistic vests used by police officers.

A spokesman for Mendelson said he hopes that D.C. Council Chairman Kwame R. Brown (D) will hold an initial vote Tuesday. But Mendelson’s advisers caution that they have no assurances that it will be pass unamended.

A majority of council members are on record as being skeptical of lessening restrictions on guns, although many have stressed that they hope to fend off more court challenges to the city’s law.