The District will pay a total of $20,000 plus attorneys’ fees to four drivers who challenged their drunken driving convictions because of inaccurate and unreliable breath test results.

Sixteen similar claims are pending in federal and D.C. Superior Court over revelations that errors and tainted court cases had doomed the old testing system.

The District admitted no wrongdoing as it finalized the deals,which grew out of an ongoing attempt by D.C. police and the Office of the Attorney General to restore a reliable breath testing program to the city.

Instead of breath tests, police and prosecutors have beenrelying on more expensive and complicated urinalysis results and roadside observations in court. The District is “hopeful” that breath test machines could be back on the streets by the fall, Attorney General Irvin B. Nathan has told the D.C. Council.

In 2010, District officials acknowledged that inaccuracies from miscalibrated equipment had overstated drivers’ breath test readings in about 400 convictions dating to 2008. The concession prompted some drivers to challenge their convictions.

Payment offers also are on the table to six more drivers who went to federal court and have until Tuesday to decide whether to accept the money or continue their cases, according to their attorney, Jeffrey L. Rhodes of Albo & Oblon.

Another 10 similar claims brought by drivers are pending in D.C. Superior Court, said Ted Gest, a spokesman for Nathan.

The District’s badly calibrated equipment would show a driver’s blood-alcohol level to be about 20 percent higher than it actually was, officials conceded in 2010. All 10 of the breath test machines used by District police produced inaccurate results.

In the District, a defendant can be convicted of driving while intoxicated based solely on a breath test result showing a blood alcohol level of at least 0.08, which makes the scores critical.

All four of the drivers who accepted the District payment had been convicted of DWI based on the machine readings, Rhodes said. They challenged those convictions after learning of problems with accuracy and reliability in the city’s testing program.

Three of the four were later convicted of driving under the influence based on evidence other than breath tests, Rhodes said. A DUI case can be prosecuted using officer observations, including outcomes during field sobriety tests such as standing on one leg. The fourth man in the cases resolved with a payment did not have another drunken driving charge brought against him after his DWI conviction was dropped, Rhodes said.

Payments to the four men ranged from $2,001 to $8,001 each, court records show.

The flawed testing acknowledged by the District did not jeopardize cases involving accidents or injuries, including fatal crashes, because blood or urine samples would have been taken as additional evidence, the attorney general’s office has said.

For more than a year after the errors were acknowledged, District officials repeatedly said they were working on a solution — and had purchased $90,000 worth of new testing equipment to salvage the program. A panel of outside national experts told city officials in October that top-to-bottom change was needed. The procedures for bringing rigorous scientific review and management to the testing, maintenance and training processes have been under design since then.

The planned improvements described by city officials would bring the District closer to the breath testing programs in Maryland, Virginia and many other states that give the responsibility to a forensic science unit.