I was listening to some generally unfunny show on Radio 4 last week, when some comedian who should really remain nameless – but whose uselessness compels me to identify him as Mitch Benn – sang a song, notionally in the style of David Bowie, on the subject of, if memory serves, farting in space.

Goodness, it was awful. As, I think, has been every supposedly comic song I’ve ever heard from Mitch Benn. It provided, though, a reminder of how awful comic songs are in general – a wake-up call that I probably needed after spending the week listening to the new album by Flight Of The Conchords.

Now I can’t pretend that I’ll be listening to this one indefinitely, much as I love the series. But “Flight Of The Conchords” works not just because it’s very funny, not just because the parodies are so lovingly meticulous (their “Bowie”, for instance, nods to about four different incarnations of the Dame with casual precision), but because Bret McKenzie and Jemaine Clement are straightforwardly good at music.

Strip away all those wry homages (and yes, it might be an easy target to mimic, but the over-enunciated Pet Shop Boys rip of “Inner City Pressure” is especially fine), and Flight Of The Conchords emerge as a pretty interesting band – mildly fey indie boys who aspire, possibly, to being a bedroom version of Hall & Oates – who just happen to tell jokes.

This is what keeps “Flight Of The Conchords” interesting, long after you’ve learned to anticipate the bit where they shout “BAGUETTE!” in terrible fake French accents during “Foux Du Fafa” (très “Les Bicyclettes De Wellington”, incidentally). When I blogged on Hot Chip’s “Made In The Dark” a few months ago, I described “Wrestlers” – tongue only partly in cheek – as a cross between Aaliyah and the Conchords.

Listening to this album, the comparison seems even more valid: the studied, wry sensitivity, the folksy take on synthpop; the pleasing suspicion that, beneath all the irony and posturing, they’re taking it all rather seriously. “Think About It” is a voluptuous parody of plaintive, conscious inner-city soul, with an anguished request – “Can someone please remove these cutleries from my knees?” – and a pointedly signposted “a capella jam”. Weirdly, though, that sense of straight-faced craftsmanship is still apparent beneath the ludicrous, over-earnest platitudes. Again, this is unambiguously fine music.

Consequently, my favourite moment on the album has no jokes, not even any words. It comes just after “Ladies Of The World”, a deliriously effete take on machismo on which they note, “We’re talking about brunettes not fighter jets”. The song ends, and then, a couple of seconds later, there’s a wordless coda of acoustic strums and helium harmonies. Comedy be damned: it’s lovely.

My favourite song from the TV show didn’t make the album, mystifyingly. “If You’re Into It” was on the “Distant Future” mini-album last year, but then so were “Business Time” and “Robots”, and they’ve made the cut here. In the spirit of sharing links and so on, here it is on Youtube.