“As a general rule, nobody has money who ought to have it,” the British statesman Benjamin Disraeli once said. That would make a good epigraph for “The Riches,” which begins its second season tonight on FX.

When it first appeared a little more than a year ago, “The Riches” was one of the more promising series on television — at least for a handful of episodes. First of all, there was the subject matter, which concerned a family of Irish Travelers, or gypsies, named the Molloys, who half-conned and half-blundered their way into assuming the identity (and the home and credit cards) of the Riches, a wealthy American couple they had accidentally killed in a car crash. Already on the run after a dispute with their own clan, they broke into the Riches’ mansion at night and woke up the next morning to discover they were now living in what passes in brochures as the gated-community version of the American Dream.

Then there were the two leads: Eddie Izzard, the wildly funny British stand-up comic and gifted improviser, played Wayne Molloy, a character who was forced to improvise constantly (though only occasionally for laughs) as he took on the identity of Doug Rich. Minnie Driver played his wife, Dahlia, a compulsively watchable drug addict, fresh out of prison. They had three kids, too: 17-year-old Cael (Noel Fisher), already a hardened thief; 16-year-old Di Di (Shannon Woodward), heading in the same direction, and the much younger Sam (Aidan Mitchel), who liked to dress up like a girl. As a family accustomed to living out of an RV, oblivious to the culture at large except when it came to exploiting it, they made a refreshing contrast to what we normally see on television.

But somehow the first season of “The Riches” fell apart, as if the show’s creator, Dmitry Lipkin, couldn’t quite nail down what the series was supposed to be about. The resulting vacuum was disguised by flurries of activity as the Molloys managed to pass themselves off as who they were pretending to be while staving off a constant series of potential disasters. Without knowing a thing about the law, Wayne got himself a job as in-house counsel to the big man in the community, Hugh Panetta (Gregg Henry), an alcoholic, semi-crazed real estate tycoon, after winning his confidence during a drunken bout of Russian roulette. (Wayne had rigged the game, naturally.) But the writers were never able to make Wayne’s transition from RV-traveling gypsy to corporate lawyer convincing. He may have been a quick study, but given his complete ignorance of the legal system, it was hard to imagine anyone keeping him on for more than a day. Somewhere around the fourth episode, belief was not merely suspended, but snapped.

Yet after watching the first four episodes of the second season, my belief has returned more or less intact. Is it because the writing has improved? The situations are more plausible? The plots less strained? I’m not sure I could answer those questions in the affirmative. (If anything, the action is more frantic than ever.) Rather, it seems to be a case of diminished expectations, and the resulting ability to sit back and enjoy what was always most pleasing about the show, which largely boils down to its leading characters.

This season they seem to be suffering from an uncharacteristic crisis of conscience. Having now lived among the “buffers” (their contemptuous term for all non-Travelers) for a while, they have grown accustomed to such luxuries as flat-screen TVs and manicured lawns. They’ve also begun, in their different ways, to wonder if a life of crime is as attractive as they’ve always regarded it.

Thanks to his friendship with his irrepressible boss, Wayne has been offered a chance to make a cool $13 million on a shady land deal. It’s far too good an opportunity to pass up, of course, and if he can just convince everyone he’s the corporate lawyer he says he is for a few more months, he may actually pull it off. Yet even as he tries to “steal” the American Dream, Wayne is buying into it like never before. Like most criminals, he has the same hopes and aspirations as everyone else — namely to live the good life, which for him includes getting his children a good education and leading them out of the Traveler rut. Even as he lies and cons his way through the day, all he’s looking for is a chance for respectability and enough money to put thievery behind him.

Whether he’ll be able to do so provides the essential tension of the series. There’s dissension within the family itself. Wayne’s eldest son, Cael, doesn’t buy into this going straight business at all. He likes stealing cars and conning people. It’s part of his ancestral pride. And then, of course, there’s Dale Molloy (Todd Stashwick), Wayne’s vengeful Traveler cousin, who’s onto his every move and is determined either to cut him down or get a 50% cut of the deal. The main flaw of “The Riches” is its clichéd view of American capitalism: rich, white, Republican, and corrupt. But introducing a family of gypsies into the mix does keep things interesting. The “haves” don’t deserve their wealth, to return to Disraeli, and nor, to be fair, do these particular have-nots. But when actors as talented as Ms. Driver and as entertaining as Mr. Izzard are on-screen, one’s inclination is to continue watching them try to get it.

bbernhard@earthlink.net