When Lucinda Williams married her manager Tom Overby in 2009, there were those who feared that America's high priestess of heartbreak might struggle to find anything to write about.

Her greatest albums, after all, are liberally scattered with unflinching accounts of unrequited love, dangerous longing and passions which briefly flare and then quickly die, usually unpleasantly. There didn't seem to be much room in the equation for wedded bliss.

It turns out Williams had similar concerns. "I was always afraid of getting committed in a marriage before," she says on the line from her home in the Hollywood Hills. "Will I be able to still write and be creative? When we first moved in together that was the big test for me – am I going to completely lose myself in a relationship or can I still be a vital artist?" And? "And we wouldn't still be together if that weren't the case. It's not as if I'm happy all the time. I mean, I love Tom and everything, but come on. It's life. Marriage is part of the process, it's not like suddenly everything else ends."

Far from career-ending, Williams has found that marriage has had a "liberating" effect on her writing. "I feel like I've stretched out more. I always wanted to try writing about different subjects, which I started doing on my last album, Blessed, with things like Soldier's Song. Anyway, songs about unrequited love are the easiest ones to write. They're a dime a dozen." For the avoidance of any lingering doubt, her twitter handle is @HappyWoman9.

Sixty this year, Williams is still adding strings to her bow and becoming ever more fearless. She has never quite found a comfortable niche, which in the beginning was a problem but now seems like a blessing in disguise. Earning her stripes in the mid-1970s in the folk clubs and coffee houses of Texas and Mississippi, her slow, stuttering trajectory has occurred without any kind of masterplan or forethought. Making music at the place where country meets folk-rock meets the analyst, for the first 20 years of her career Williams bounced between numerous record companies, none of which seemed to know what to do with her or her songs of hard drinking, suicide and dark romance.

She finally made a breakthrough in 1998 with Car Wheels on a Gravel Road, the album which won her the first of three Grammies. "That was the one," she agrees, although it wasn't until the follow-up, Essence, in 2001, that she felt truly in command of her recorded work. It coincided with her finding a settled home at Lost Highway, getting bigger budgets and a good publishing deal, all of which gave her the stability to release better records more frequently. "I had been playing for 15 years, but I still wasn't used to the whole process of writing, recording and touring," she says. "Now that process is much easier, but the earlier albums are more low-budget, and I didn't feel that I had control. I always wanted my records to sound like The Pretenders, I wanted Chrissie Hynde's big in-your-face vocal sound. Mine always sounded kind of little and thin."

There are many ways to describe the extraordinary Velcro rasp of Williams's vocals, but neither "little" nor "thin" is one of them. Like the spare and at times uncomfortable honesty of her writing, that grit-and-glue voice is not for everyone, but those who love her tend to do so with a passion. For devotees, her catalogue belongs to the same lineage of unique and distinctive American songwriting as Tom Waits, Willie Nelson and Bruce Springsteen.

Williams is visiting Scotland to play a couple of concerts billed as "intimate", although anyone who has seen her perform will know that intimacy tends to come with the ticket. It will, however, be a chance to catch her in a more exposed musical setting, playing with just the accompaniment of David Sutton on bass and Doug Pettibone on guitar. The stripped-back trio format is, she concedes gamely, largely dictated by economics, "but it ends up being an artistic choice, too. It becomes a different thing. We can do pretty much any of my songs, and they always end up coming out a little differently, which I like."

Over five nights recently in Minneapolis she played 70 different songs, including some new ones. "I always love doing the brand new songs, that's always challenging and keeps it really fresh for me," she says. She tends to write in the kitchen, a room which has clearly been getting a lot of use recently. "I have about 40 new songs in various stages of completion. I think I'm getting more prolific than I've ever been, just from experience I guess."

The "intimate" tour is a pit stop between albums, coming two years after Blessed and shortly before she goes into the studio to record the next one. The release of Blessed brought to an end her contract with Lost Highway, and she is one of the few artists in the industry currently fielding offers. "I'm in a great bargaining position, and I know that's an anomaly in this day and age," she says. "I'm just really excited because people want me, and, that hasn't always been the case."

Lucinda Williams plays Perth Concert Hall tomorrow and Queen's Hall, Edinburgh, on Sunday.