I discovered Lyle Lovett when he did a session for Andy Kershaw’s radio 1 show in the late 1980s. There were four tracks, spread across the show, and from the very beginning of the first one, You Can't Resist It, I was hooked. The session featured just Lovett and cellist John Hagen, and I’ve yet to find a recorded version of the song that lives up to the spellbinding effect of my first exposure to the song, although I’ve seen the pair recreate it on more than one occasion live in concert. I was tempted to weave him into Dead Man Singing, but somehow couldn't find a space for him.

Lovett was part of the 80s Alt-Country revival, along with the likes of Dwight Yoakam and k.d. lang, and Pontiac (1988) was his second album. It opens with another song from that Kershaw session, and one that would be in contention for a place if ever I was called upon to choose my Desert Island Discs: If I Had a Boat. I was instantly taken with the song on that first hearing, a playful, almost irreverent, confection about wishing to have a boat, and a pony, and to ride the latter on the former. Over the years I’ve come to realise that behind the whimsical deadpan lyrics lies a heartfelt paeon to freedom, and one of the most subtly meaningful songs in the country canon.

Lovett glides elegantly through different styles, from doleful acoustic ballads to country swing, from honky-tonk to jazz. Country royalty Emmylou Harris turns up on Walk Through the Bottomland, while tongue-in-cheek offerings like She's Hot To Go or She's No Lady use humour – sometimes aimed at the singer himself – to undercut what in other hands could come across as sexism. In the former, we are told, ‘The preacher asked her, and she said “I do”. The preacher asked me, she said, “Yes, he does too.” The preacher said, “Son, I pronounce you 99 to life. She’s no lady, she’s your wife”.' Similarly, She's Hot To Go sees the singer excitedly describing the visual charms of a lady who has caught his eye, until she turns round and the lyric turns to a panic-stricken repetition of the fact that she’s ugly. A quick drum fill later, one of Lovett’s band responds with ‘Well you’re ugly too’, which sees the singer dismiss his remaining objections and return to enthusiastic admiration and desire.

Set against that humour, there are songs of quiet understatement that suggest a deep hinterland of emotion. Simple Song and Pontiac, for example are textbook examples of the less is more school of thought, powerful and hard-hitting yet gossamer thin if you were to start dissecting them. Any attempt to pigeonhole Lovett on the basis of his songwriting, whether stylistically or lyrically, is doomed to fail. He turns his hand to an eclectic mix of styles and subjects and effortlessly masters all of them.

Perhaps the song on the album that best stands up to the vast shadow cast by If I Had a Boat is LA County. I’ve seen Lovett perform it live on a number of occasions, and it says something for a song if even the ad hoc introduction sticks in the memory decades later. I remember Lovett once explaining that, ‘Whenever I write a song, one thing I always try to remember is to make myself look as good as possible,’ before pausing for a perfectly judged beat and adding, ‘With this one, I’m not sure what went wrong.’ If you listen to the song, with its gradually unravelling storyline of lost love and a murderous road trip, you’ll see what he means.

Lovett himself is more familiar to non-country fans as the voice who duets with Randy Newman on You've Got a Friend In Me at the end of Toy Story 2 (1999), as a sometime actor – he had parts in The Player (1992) and Short Cuts (1993), among others – and as a former husband to Julia Roberts. I remember seeing him play Hammersmith Odeon at one point in the 1990s where an irritating American woman some rows behind me kept calling stuff out between songs. Lovett seemed graciously indulgent rather than nipping her interruptions in the bud, and when news broke of his marriage to Roberts not long after, I wondered whether the irritating American had been, in fact, the world famous actress. Lovett himself is no oil painting (as he reminds us in She's Hot To Go), and I remember as a single man at the time feeling that if he could marry Juliet Roberts, it gave hope to us all.

But Lovett deserves to be remembered in his own right. If he managed to punch above his weight in looks, he was certainly Ms Roberts’ equal in terms of talent. As a performer and – especially – a songwriter, he deserves to be much more widely hailed. One review of Pontiac describes it as ‘a terrific showcase of his subversive and idiosyncratic country style’, with its songwriting ‘landing somewhere between magical realism and creative nonfiction’. That’ll do for me.