I really expected more garter belts in Howard Chaykin's Justice League.

Well, they're all business in these issues, so maybe not. From 2006, JLA: Classified #26, "Secret History, Sacred Trust, part one" Written by Howard Chaykin, pencils by Kilian Plunkett, inks by Tom Nguyen.  

I think this was pretty concurrent with the JLA book at the time, with the Grant Morrison core team: the most seasoned of professionals, if a bit detached. They were like an encounter with a really good paramedic: if you need them, you're probably confused, helpless, and having the worst day of your life; but for them it's just Tuesday. They'll take care of you, but won't get all worked up about it.

Plotwise, this is both pretty solid and almost specifically what you would expect from Chaykin: two South American countries were on the verge of war, but both sides seem to somehow have put metahuman soldiers into the field. The JLA has to thread the needle between doing the right thing, and not overly imposing their will on foreign nations, while maybe also figuring out where the metahumans came from and not seeming too pro-America. Despite having two aliens and two monarchs on the team, they still work more closely with the U.S. government than you would probably expect; which feels real post-911 but also hopefully isn't rushing back. It's also completely not-surprising that the President is concerned about any other countries "using metahumans for international terrorism" yet being A-OK with America having them.

From Joe Kelly's run, Faith makes an appearance here, returning from the warring countries "on a mission I can't discuss for an agency that doesn't officially exist." (I honestly forget what her powers were, and I think she was traded to the Byrne-era Doom Patrol, which really feels like getting sent to the minors.) While in the field they might have been a unified front, the League seems a little back-bitey here: Kyle and Wally are seen by some of the others as a bit like children, American simpletons who don't really understand the rest of the world, no matter how many times they've saved it. (...fair.) Later, playing the king card, Aquaman throws a wrench in things, by insisting the President and the JLA make their case to the United Nations; where things get dragged to a halt by the objections of the Dutch ambassador. (Are her complaints legitimate, or somehow sinister? Maybe both, really.) While the JLA is officially ordered to stay out of the conflict, Faith takes Bruce, Clark, Kyle, Wally, and Diana undercover; on Mission: Impossible rules: if you're caught, no one's ever heard of you... 

This storyline would run through JLA Classified #31, and while I was able to get the whole thing from the dollar bins recently, I don't think it's been collected. Later in the story, J'onn plays one-man JLA to make it look like the others were where the world expected them to be; Kyle is effective undercover at a comic-con while Wally seems really bad at clandestine stuff; and the JLA honestly seems to get along pretty well regardless of if they're sometimes irritated or annoyed by each other.