A few minutes before they were seen fleeing the corner where New Orleans police Officer Jonathan Smith was shot early Sunday morning, Cornelius Barthelemy and James Wilson sped away from a home a few blocks away in the 7th Ward after a man was shot in the neck during a party, police said Wednesday.

Now, in addition to the previous counts of first-degree murder and attempted murder of a police officer, Barthelemy and Wilson are facing new counts of aggravated battery and illegal use of weapons.

The earlier shooting happened about 1:35 a.m. Sunday at a home in the 1300 block of Annette Street in the 7th Ward, about six blocks from the corner of St. Claude and Elysian Fields avenues, where Smith was shot while working an off-duty detail.

Police said that in the first incident, a 28-year-old man was shot in the neck while leaving a house party.

While investigating that incident, detectives matched witnesses’ descriptions of the unknown men who fled after the shooting with Wilson, 26, and Barthelemy, 34. It was not immediately clear whether Barthelemy or Wilson is the suspected gunman in that case.

Witnesses also told police that the men responsible for that shooting fled the scene in a white Ford Expedition, the same type of vehicle used to whisk away the suspects in the subsequent shooting of the police officer.

At 1:42 a.m., Barthelemy allegedly pointed a gun at Smith and fired several shots as he stood in front of Gene’s Po-Boys. Smith returned fire, sending eight bullets in the direction of Barthelemy and a third suspect, 36-year-old Caesar Adams.

The motive for the shooting of Smith is not clear.

According to court documents, Wilson told police that Barthelemy was driving through the neighborhood and set his sights on Smith for some reason. “I’m ’bout to kill this cop,” Barthelemy said before parking the SUV and getting out, Wilson told police.

Barthelemy and Adams apparently were each struck by Smith’s fire.

Wilson remained in the SUV during that confrontation and was not wounded.

Adams was found dead a few hours later in the back of the SUV. It’s is not yet clear whether he died from a wound suffered when he was struck by a bullet from Smith’s gun or if he was shot and killed later.

While Barthelemy was in a hospital to treat his wound, investigators showed him surveillance images that captured him and Adams outside the store at the time of the shooting. Barthelemy, police have said, acknowledged he is the man in the images but said he doesn’t remember being at the corner that morning.

Barthelemy and Wilson each were booked on counts of first-degree murder and attempted first-degree murder of a police officer in connection with Smith’s shooting and Adams’ death.

Wilson had told police that he, Barthelemy and Adams were at a house party before they drove to the po-boy shop but that he did not know where the party took place because he is not familiar with New Orleans. He lives in Port Sulphur.

Smith’s quick draw when challenged probably saved his life, his commander said Wednesday.

“Faced with the circumstances he was faced with, his training and his experience really paid off for him,” 5th District Cmdr. Christopher Goodly said during a weekly crime statistics meeting.

Smith continued to recover Wednesday at Interim LSU Hospital. Although he is doing well, he is “still severely injured,” Goodly said. “All the disadvantages (of an ambush) and ... he came out on top of that.”

Because Smith likely will be off the job for weeks, if not months, Goodly asked his officers to consider donating money as part of an in-house fundraiser for him.

“He was working a detail, so I know that actually affects his livelihood. He’ll probably not be able to work details for a little while as he rehabilitates,” Goodly said. “So we’re going to do our normal family thing and try to do a little collection for him to keep him going.”

Follow Danny Monteverde on Twitter, @DCMonteverde.