Richard Thompson albums come in two basic varieties. On the one hand, you’ve got your albums that show, in one way or another, a kind of conceptual backbone — be it a narrative one (like his album-length exploration of suburban malaise, Mock Tudor) or stylistic (like his homage to traditional British folk, Front Parlour Ballads). On the other, you’ve got those albums that are simply collections of Richard Thompson songs — some of them great (The Old Kit Bag), some merely good (Sweet Warrior). Falling somewhere in between: his Mitchell Froom-produced albums of the ’90s, which weren’t necessarily united in style or subject matter but were certainly focused and uniform in their sound.

Also falling somewhere in between — and in some ways capturing the best of both worlds — is Dream Attic, Thompson’s first new recording in three years. There is no narrative running through these songs, and they seem written to emphasize Thompson’s eclecticism over all else; there are folk numbers intermingled with rock songs, love songs interspersed with political satires. So in that sense, the album is nothing more or less than a collection of Richard Thompson songs — something that’s always welcome.

But wait. What you’re hearing is not exactly a batch of sturdy new Thompson compositions in the vein of Sweet Warrior; what you’re hearing, rather, is essentially a live rehearsal. These tracks were all cut live on the floor, with Thompson fronting a five-piece band, in front of a small audience. You wouldn’t necessarily know that at first blush, were it not for the applause that briefly follows each song. Yet it is a dynamic that informs everything about this record — the sometimes exhilarating and sometimes frustrating sound of a band feeling their way through a batch of new material.

It’s a tight band — Thompson on guitar; Joel Zifkin in violin and mandolin; Michael Jerome on drums; Taras Prodaniuk on bass; and Pete Zorn on various saxes and flutes — and Thompson uses them wisely, often restraining them to the point where the music sounds almost as spare as the bare-bones trio recording The Old Kit Bag, but sometimes unfurling them in jammy rock ecstasy. That there is a certain jam band quality to some of these tracks is as much evidence of the band’s enjoyment of each other as the relative newness of the material, something that sometimes yields rough, unfinished results. On “Among the Gorse, Among the Grey,” Thompson and the band seem to be aiming for something along the lines of John Martyn’s spacey, esoteric folk, but without his pop sensibilities to anchor them the song just becomes sort of formless. Some of the more jam-centered tracks meander in much the same way — which is especially annoying when the songs slip past the six- and seven-minute markers, as they frequently do.

But when Thompson is on, he’s on. The best moments here are the ones where the songs really take on flesh and hold together as examples of Thompson’s superb sense of craft. The highlights seem to come in pairs, two sides of the same coin: “Haul Me Up” is a tough rock and roll sing-along with a bit of a country gait to it, and is followed immediately by the haunting, mystical folk of “Burning Man,” a spiritual cousin to the Old Kit standout “A Love You Can’t Survive.” “Here Comes Geordie” indulges in Thompson’s love for trad-folk, this time all decked out in flutes and whistles, while “Demons in Her Dancing Shoes” is a wickedly fun Thompson rocker. These songs — along with the kickin’ groove of “The Money Shuffle” and the bright, crowd-pleasing pop of “Big Sun Falling in the River” — are as good as you’d expect from Richard Thompson, and reminders of why just another batch of Thompson songs is such a treat.