To the annals of great sibling duos, we can add: Lindsey Buckingham and Christine McVie. Of course, these two aren’t remotely related, even by nationality, much less blood. But now that they’re working together as a couple for the first time after 40-plus on-and-off years in a famously larger ensemble, there’s a highly non-dysfunctional family dynamic at play in the pairing. An hour and 40 minutes spent in their company is as relaxing as hanging out with a particularly agreeable brother and sister who’ve retired to the bar right after a bigger and tenser family reunion.

Los Angeles just had that family reunion in the form of Fleetwood Mac’s headlining show at the Classic West festival at Dodger Stadium. Two and a half weeks later, Buckingham and McVie were back in L.A., playing the Greek Theatre as part of a joint amphitheater tour that’s the mainstay of their year, taking place before and after Mac’s two one-off stadium shows. It’s no disparagement of any of the absent members of Fleetwood Mac to say that — sometimes, at least — less is just a little bit more.

There was more overlap with the recent Fleetwood Mac show than one might have expected, not just in the set list, which did include nine Mac numbers, but in the arrangements of those tunes. It does make sense that if you’re going to include “Tusk” in your set, you’re probably going to hire a drummer who pounds the skins as flayingly as Mick Fleetwood — in this case, wild-haired session monster Jimmy Paxson. (It’s less sensible that they felt the need to make up for Stevie Nicks’ missing backups on “Little Lies” by throwing in what sounded like a programmed female vocal part, in a case of fidelity that actually became distracting.)

If they wanted the full-band Fleetwood Mac songs to sound as much like Fleetwood Mac as possible, that was probably meant at least in part to ease the crowd into the wealth of new material performed. The duo played seven out of 10 songs from their new “Lindsey Buckingham/Christine McVie” album, but these all had such an aura of familiarity that the crowd didn’t need much greasing to ease into the fresh stuff. It’s a Nicks-less Mac album, for most intents and purposes, and if they hadn’t announced “Sleeping on the Corner” as the first of the new songs, most of the crowd would have assumed it was a “Tango in the Night” single they’d forgotten a few synapses ago.

Buckingham tried to provide some narrative through the show — about how McVie rejoined Fleetwood Mac, and about the new album, slightly skirting the issue of why this didn’t end up being a Mac album. “The first surprise happened a couple of years back, and as I’m sure most of you know, Christine had taken leave of the band Fleetwood Mac for… how long?”

“It was a long time, 15 years,” McVie answered, in one of the short interjections she added to Buckingham’s speeches. “What was I doing all that time?”

Christine McVie

“…And the second surprise was that as a byproduct of (rejoining the group), she began getting back into her own creative process and sending me bits and pieces of song ideas across the pond from London over to Los Angeles. Of course me being me, I had my way with them….”

And therein lies part of the reason why they work well as a duo: McVie has always been the most recessive of the three lead presences in Fleetwood Mac, and you don’t imagine her having much problem with Buckingham applying all the studio wizardry he can muster to the material she brings. You saw it on stage in “Too Far Gone,” probably the thinnest of the new songs, which suddenly becomes a powerhouse with the addition of some “Tusk”-like drum breaks that transform the tune into something more galvanizing. On the other hand, the harmonic presence of McVie undoubtedly helps reinforce Buckingham’s lusher instincts, which come to an ideal head in a mixture of emotion and musical layering like the new “In My World.”

After the predictability of that Classic West show, the more adventurous bookending of this Greek appearance helped make it feel like something special and thought out. The show might actually have peaked with its first four numbers, which had Buckingham and McVie alone on stage, getting into amped-down “Trouble” and reviving FM’s lesser remembered “Wish You Were Here.” At the end, they indulged in what might have come off as an anti-climax after the inevitable “Go Your Own Way,” ending the show with a couple of final tracks from the new album.

Surely it’s tempting fate, or traditional audience tolerance, to announce you’re done playing the oldies and will finish out the encore with two tracks the majority of the crowd hasn’t heard. When McVie further warned before that last number, the sweetly earnest “Game of Pretend,” that it was “a ballad — (and) it’s not ‘Songbird’,” you would have really expected an eighth-inning-style rush to the parking lot. There wasn’t so much in the way of early exiting, though. If, at this reunion, McVie represented the cool, stabilizing older sister and Buckingham the rambunctious youngest brother, there was a full house of middle children wanting to stick around and enjoy the serene family symbiosis as long as possible.